Is there a difference between “co-redeemer” and “co-redemptrix”?
Technically co-redeemer is masculine and co-redeemptrix is female.
A woman whose participation is believed by some Roman Catholics to be essential for the redemption of humanity
Specifically: Virgin Mary
The title of co-redeemer is occasionally applied the the Virgin Mary:
Mary's title of Co-Redemptrix or Co-Redeemer can assist in magnifying our understanding of God's humility. - Teachings Not Yet Declared Dogmas Co-Redemptrix or Co-Redeemer
Yes, it seems Pope Francis did throw cold water on any hope for a 5th Marian dogma!
At his weekly public audience on March 24, 2021, Pope Francis rejected the claim that the Virgin Mary should be honored as “co-redemptrix,” saying that she should be honored, “but as a mother, not as a goddess, not as co-redeemer.” Noting that he was speaking on the eve of the Annunciation feast day, he pointed out that in Christian iconography, the depiction of Mary is “always in relation to her Son and in connection with Him.. she always points out the center: Jesus.” - Catholic News Headlines
Although Pope Francis was not speaking ex cathedra, he definitively makes a point that he does not favour such a dogma.
Christ is the Mediator, Christ is the bridge that we cross to turn to the Father (see Catechism of the Catholic Church, 2674). He is the only Redeemer: there are no co-redeemers with Christ. He is the only one. He is the Mediator par excellence. He is the Mediator. Each prayer we raise to God is through Christ, with Christ and in Christ and it is fulfilled thanks to his intercession. The Holy Spirit extends Christ’s mediation through every time and every place: there is no other name by which we can be saved: Jesus Christ, the only Mediator between God and humanity (see Acts 4:12).
Due to Christ’s one mediation, other references Christians find for their prayer and devotion take on meaning, first among them being the Virgin Mary, the Mother of Jesus.
She occupies a privileged place in the lives of Christians, and therefore, in their prayer as well, because she is the Mother of Jesus. The Eastern Churches have often depicted her as the Odigitria, the one who “shows the way”; and the way is her Son, Jesus Christ. The beautiful, ancient painting of the Odigitria in the Cathedral of Bari comes to my mind. It is simple. The Madonna who shows Jesus, naked; then they put a shirt on him to cover his nakedness, but the truth is that Jesus is naked, he himself, man, born of Mary, is the Mediator. And she indicates the Mediator: she is the Odigitria. Her presence is everywhere in Christian iconography, sometimes very prominently, but always in relation to her Son and in connection with Him. Her hands, her eyes, her behavior are a living “catechism”, always indicating the hinge, she always points out the center: Jesus. Mary is completely directed toward Him (see CCC, 2674) to such an extent that we can say she is more disciple than Mother. The directions she gave at the wedding at Cana: “He: do whatever he will tell you”. She always refers to Christ. She is the first disciple.
This is the role Mary fulfilled throughout her entire earthly life and which she forever retains: to be the humble handmaid of the Lord, nothing more. At a certain point in the Gospels she almost seems to disappear; but then she reappears in the more crucial moments, such as at Cana, when her Son, thanks to her caring intervention, performs his first “sign” (see Jn 2:1-12), and then on Golgotha at the foot of the cross. - General Audience, 24.03.2021
Wikipedia has the following to say about the title of co-redemptrix:
According to those who use the term, Co-Redemptrix refers to a subordinate but essential participation by the Blessed Virgin Mary in redemption, notably that she gave free consent to give life to the Redeemer, which meant sharing his life, suffering, and death, which were redemptive for the world. Related to this belief is the concept of Mary as Mediatrix, which is a separate concept but regularly included by Catholics who use the title Co-Redemptrix. A Fifth Marian Dogma has been proposed including both Mediatrix and Co-Redemptrix.
The term Co-Redemptress was used by Pope Leo XIII in 1894. "For in the Rosary all the part that Mary took as our co-Redemptress comes to us..."
The concept was especially common in the late Middle Ages, when it was promoted heavily among the Franciscans, and often resisted by the Dominicans. By the early 16th century the hopes of the concept becoming Catholic doctrine had receded, and have never seriously revived. In more recent times, the title has received some support from the Catholic Magisterium though it is not included in the concluding chapter of the apostolic constitution Lumen gentium of the Second Vatican Council, which chapter many theologians hold to be a comprehensive summary of Roman Catholic Mariology. Some, in particular the adherents of the Amsterdam visions, have petitioned for a dogmatic definition, along with Mediatrix, and the process for further theological clarification and eventual dogmatic definition is ongoing. Pope John Paul II was the most favorable of recent Popes. As a Cardinal, Pope Benedict XVI suggested that the Marian title caused confusion and did not sufficiently reflect scripture. Pope Francis has repeatedly suggested the title not be used. - Co-Redemptrix
There is no difference; Redemptor (Redeemer) and Redemtrix (Redemptress) are simply the Latin for Redeemer in the masculine and feminine forms.
The Council of Trent (a Council as yet unrivaled in terms of authority) authoritatively taught that Christ is quote, "alone our Redemmer and Saviour" (Session XXV, emphasis mine; note that this doesn't preclude 'co-redeemers in the sense described below).
One can admit and accept the doctrine that Mary is 'co-redemptrix' if and when one understands it to be identical with the doctrine - the clearly and indisputably apostolic doctrine - that Mary is the new Eve. Even indisputably and uniquely and markedly co-operated in our damnation, and Mary indisputably and uniquely amd markdely in our Redemption from said.
As noted in Ken Graham's answer, Pope Francis does very explicitly reject the doctrine by that name. However, what he says is not (and may not be) opposed to the apostolic and dogmatic idea that Mary is the new Eve, and as such plays the most importantly co-operative role with the Saviour in Redemption just as Eve played the most important role next to the Damnator with regard to the Fall.
"Redemptrix" (English: "redemptress") is the feminine version of the masculine "redeemer".
The Redeemer is Jesus Christ. The Co-Redemptrix is His Blessed Virgin Mother:
A title of the Blessed Virgin as co-operator with Christ in the work of human redemption. It may be considered an aspect of Mary's mediation in not only consenting to become the Mother of God but in freely consenting in his labors, sufferings, and death for the salvation of the human race. As Co-Redemptrix, she is in no sense equal to Christ in his redemptive activity, since she herself required redemption and in fact was redeemed by her Son. He alone merited man's salvation. Mary effectively interceded to obtain subjective application of Christ's merits to those whom the Savior had objectively redeemed.
Yes, there is only one Mediator (1 Tim. 2:5), but that does not mean there aren't other mediators subjected to Him. Think about who brought you to Christ. You didn't do it alone. Saints and angels in heaven plus people on earth can help you through their prayers and actions. These people are your mediators, being subject to the one Mediator.
The Blessed Virgin Mother of God is Mediatrix because without her "Be it done to me according to thy word" (Luke 1:38)—her fiat—there would be no Christ, no Church, and thus no salvation. She brings us to Christ and Christ to us in a most supreme way than any other creature can.
Is there a difference between “co-redeemer” and “co-redemptrix”?
The clear answer is none.The meaning or role as Co-redeemer & Co-redemptrix means cooperation by either male or female, but the meaning and action is basically the same.
Did Pope Francis throw cold water on any hope for a 5th Marian dogma or is there a fundamental difference between "co-redeemer" and "co-redemptrix" that leaves the door slightly ajar?
Did Pope Francis throw cold water? On the surface, the answer is Yes, but a deeper understanding must be reflected on Pope Francis inspiration in proclaiming the Catholic faith, as he said;
"Faith is propose and not impose."- Pope Francis
Pope Francis advocacy is "journeying together" with Christian and Non-Christian, and the Church mission is for the People of God including Jews, Muslims, Buddhist, Hindus, etc. is to encounter Jesus Christ and Mary's role in the Church thru their own personal encounter.
Pope Francis inspired mission is unity & fraternity, and Our Lady like St.Therese of Liseux said, "She is more Mother than Queen".
Our Lady embraced Motherhood of Christ the Redeemer first and Pope Francis cited Mary's own humble admission of Herself being the "handmaid of the Lord", and not seeking any titles because She is the humblest creature of all, eventhough She deserves all the title. But the Magnificat, saying "all generations shall call Her blessed" means, She will be crown with many titles, and the Fifth Dogma is a fitting title for Mary's role. But Pope Francis was not yet inspired by the Holy Spirit to focus on Marys's role as Co-redeemer or Co-redemptrix, the clear inspiration and direction of the Church is towards unity of all Christian and Non Christian thru fraternal charity as evident in Pope Francis latest teachings on "Fratelli Tutti" calling all the People of God as "All Brothers". Like Pope Francis signing with our Muslims brothers the fraternal agreement and add to that his recent visit to Iraq.
APOSTOLIC JOURNEY OF HIS HOLINESS POPE FRANCIS TO THE UNITED ARAB EMIRATES (3-5 FEBRUARY 2019) A DOCUMENT ON HUMAN FRATERNITY FOR WORLD PEACE AND LIVING TOGETHER http://www.vatican.va/content/francesco/en/travels/2019/outside/documents/papa-francesco_20190204_documento-fratellanza-umana.html
ENCYCLICAL LETTER FRATELLI TUTTI OF THE HOLY FATHER FRANCIS ON FRATERNITY AND SOCIAL FRIENDSHIP http://www.vatican.va/content/francesco/en/encyclicals/documents/papa-francesco_20201003_enciclica-fratelli-tutti.html
In closing the wisdom behind Pope Francis not focusing more on Mary's other titles and simply focus on Her Motherhood role as evident in his elevation of Mary's title as "Mother of the Church" into a feast celebration. The 5th Dogma has Catholic foundation, but accepting Mary's role as Co-Redemptrix, Advocate and Mediatrix must be accepted not only by Catholic but also by the People of God that includes Protestant, Christian,Jews, Muslims, Buddhist, Hindus, etc. It is more wise to proclaim the 5th Dogma having the support of Christians and Non Christian thru their own personal encounter of the role of Mary played in the salvation of man. And this can only be realize not by imposing the Catholic faith on Mary's role but by proposing it along the Christain journey of all our brothers in Christ shining the teachings in Fratelli Tutti, Muslims Fraternal Agreement, and affirming "Ecumenism and Nostra Aetate" a teachings in the Vatican II Council.
Our Lady will wait for the perfect time, and in God's perfect time to proclaim the 5th Marian Dogma, after all the People of God had achieved unity thru fraternal charity inside the Church founded by Christ to fulfill the desires of the Father in John17:20-22.
IMPORTANT NOTE : My conclusuon and personal views was in harmony with the answer of Father Stefano de Fiores, professor of Mariology at the Pontifical Gregorian University in Rome . Here's the source of his interview explaining the primary reason was "Ecumenism & Fraternal charity" and not a theological one, as unity and fraternity must be the focus first like what Pope Francis is doing now, and it is the Christian and Non-Christian participation in imploring Mary's role that will bring about the perfect timing in proclaiming the 5th Marian Dogma. https://udayton.edu/imri/mary/c/co-redemptrix-as-dogma.php