Although this very related question about the marks of the true church in Reformed Theology has already been asked, my question is whether other Protestant traditions or Catholicism have an equivalent set of requirements for what they consider the true church?
In Catholicism, the marks of the Church are that she is
these words are taken from the second part of the Nicene creed, which is commonly prayed at every Mass and the tenents of which are generally accepted by mainline Protestant denominations.
I think, but have very little basis for this thought, that Protestant reformers used the word Marks to mean something different. And perhaps it means something different coming over to English from Latin as well as German, we just had one word that meant two totally separate things
Catholics use them as adjective to describe their Church, not as adjectives to describe the ideal church because they know that even though the Church is composed of fallen members, she is the ideal and would continue to be the ideal even if she had no members left alive.
Mainly for historical interest, I point out Optatus, a bishop of Milevis in modern-day Algeria. In a work published some time around A.D.370, he wrote at length in opposition to Parmenianus, the bishop of Carthage and leader of the Donatist movement.
Parmenianus claimed that there were six distinctive gifts of the true Church, and that Donatism possessed them. Namely, Cathedra, Angelus, Spiritus, Fons signatus, Sigillum, and Umbilicus. Cathedra ("chair") refers to a bishop's see. Angelus ("messenger"/"angel") is one of the ancient titles for a bishop (consider the "angels of the churches" in Revelation). Spiritus is the Holy Spirit. Fons signatus ("sealed fountain") is a reference to baptism, and sigillum ("seal") is the Christian creed. Umbilicus ("navel") is a reference to the altar.
Optatus agreed with the first five, but rejected umbilicus. The Cathedra he said was the see of Peter, and he traces the lineage of Roman bishops. The Angelus goes with the Cathedra. The Spiritus cannot be shut up in a small corner of Africa, and therefore cannot belong to the Donatists. The Fons and Sigillum go hand in hand.
Note that Optatus himself subscribed to the Nicene creed. However, at the time this work was published, the Nicene creed had not yet been amended by the first Council of Constantinople to include the passage listing four marks of the Church (one, holy, catholic, and apostolic). It is unlikely that he would have disagreed with the Constantinopolitan formulation, nor that the council would disagree, for instance, with the statement that the Holy Spirit is one of the gifts of the Church. Ultimately, there's more than one way to interpret the question ("what distinguishes the true Church?"), and more than one way to formulate an answer.