Interestingly enough, it was not until about 50 years ago in the Sixties that the Roman Catholic Church renamed itself as the Catholic Church. We will get to that, but first here’s a summary background on church terminology as it changed over the centuries from “wherever Christ is” to the self-identified Catholic Church with the Pope at its head. Early dates are estimates.
• 110 CE catholic church wherever Christ Jesus is
• 110 CE catholic church in Smyrna and everywhere
• 150 CE church of God at XYZ city, like Rome or Corinth
• 200 CE catholic church everywhere
• 400 CE Roman Church self identifies
• Centuries of Roman Church and catholic church and Roman Catholic terminology
• 1950 Roman Catholic Church last usage
• 1965 Catholic Church (those in communion with the Pope) first usage
CATHOLIC ABOUT THE WHOLE
To expand on these changes, the first mention of catholic church is in the Ignatian letters written about 110 CE. Catholic means “about the whole” https://en.wikipedia.org/wiki/Catholic_(term). This first grouping is from roughly 110 CE to about 160 CE.
[Ignatius] The Church of God which sojourns at Smyrna, to the Church of God sojourning in Philomelium, and to all the congregations of the Holy and Catholic Church in every place:
http://www.ccel.org/ccel/schaff/anf01.iv.iv.html
[Polycarp’s martyrdom] all the people wondered that there should be such a difference between the unbelievers and the elect, of whom this most admirable Polycarp was one, having in our own times been an apostolic and prophetic teacher, and bishop of the Catholic Church which is in Smyrna.
http://www.ccel.org/ccel/schaff/anf01.iv.iv.xvi.html
[Ignatius] wherever Jesus Christ is, there is the Catholic Church.
http://www.ccel.org/ccel/schaff/anf01.v.vii.viii.html
[Clement’s epistle] The Church of God which sojourns at Rome, to the Church of God sojourning at Corinth,
http://www.ccel.org/ccel/schaff/anf01.ii.ii.i.html
[Polycarp’s epistle] Polycarp, and the presbyters with him, to the Church of God sojourning at Philippi
http://www.ccel.org/ccel/schaff/anf01.iv.ii.html
Ignatius, who is also called Theophorus, to the Church of God which is at Philippi
http://www.ccel.org/ccel/schaff/anf01.v.xvii.html
ALL BUT
About 50 years later, during the debate on the validity of the baptism by heretic question, the reiteration of the idea that the whole church is catholic remains. Oddly, it is alleged that every church is catholic, but not the one led by Pope Stephen!
Cyprian’s council in which everyone claims to be the Catholic Church.
http://www.ccel.org/ccel/schaff/anf05.iv.vi.i.html
And yet on this account there is no departure at all from the peace and unity of the Catholic Church, such as Stephen [of Rome] has now dared to make;
http://www.ccel.org/ccel/schaff/anf05.iv.iv.lxxiv.html
ROMAN CHURCH and ROMAN CATHOLIC CHURCH
Roughly another 200 years later to circa 400 CE the church at Rome begins to identify as the Roman Church.
Gregory, a servant of God, presbyter and abbot of the monastery of Saint Theodore in the province of Sicily constituted in the territory of Panormus, has given us to understand that men of the farm of Fulloniacus, which belongs to the holy Roman Church,
http://www.ccel.org/ccel/schaff/npnf212.iii.v.i.viii.html
Then follow four books which I [Augustine] wrote to Boniface, bishop of the Roman Church,
http://www.ccel.org/ccel/schaff/npnf105.xviii.ii.html
For the next 1,300 years, we continue to find that idea of the church at Rome, excepting the Schism, as the Roman Church. And then it begins to show up again as the Roman Catholic Church. For example in 1870 at the Second Session of the First Vatican Council, the Roman church uses that moniker to refer to itself as part of the overall catholic church.
I, Pius, bishop of the catholic church, with firm faith believe and profess each and every article contained in the profession of faith which the holy Roman church uses, namely:
http://www.papalencyclicals.net/Councils/ecum20.htm
Finally, in 1943 referring to an earlier institute, we find the idea that the Roman Church is positioning itself as the Catholic Church.
… finally "in order that a center of higher biblical studies might be established in Rome, which in the best way possible might promote the study of the Bible and all cognate sciences in accordance with the mind of the Catholic Church" he [Pope Pius X] founded the Pontifical Biblical Institute,
http://www.papalencyclicals.net/Pius12/P12DIVIN.HTM
Moreover in 1951, we find the idea that the Catholic Church in Rome is the mother of all.
- With all the more reason, then, does the Catholic Church, most loving mother of all men, call on all her children to be zealous in helping these intrepid missionaries by their offerings, by prayer and by fostering missionary vocations.
http://www.papalencyclicals.net/Pius12/P12EVANG.HTM
CATHOLIC CHURCH with POPE AT HEAD
In fairly quick succession, the idea continues and forms. In 1964 the idea that Rome is the Catholic Church appears to be first clearly promulgated
We beg the separated brethren to consider the inconsistency of this position, not only in that, without the Pope the Catholic Church would no longer be Catholic, but also because, without the supreme, efficacious and decisive pastoral office of Peter the unity of the Church of Christ would utterly collapse.
http://www.papalencyclicals.net/Paul06/p6eccles.htm
Lastly, according to this Wikipedia article,
The use of "Catholic Church" is usually preferred by the Holy See and most of its adherents. The last official magisterium document to use "Roman Catholic Church" was issued by Pope Pius XII in 1950.[14] "Catholic Church" was used by Pope Paul VI when signing the documents of the Second Vatican Council.[15] [held 1962-1965] This preference also usually appears on the website of the Holy See. In the Catechism of the Catholic Church, only "Catholic Church" is used.
https://en.wikipedia.org/wiki/Roman_Catholic_(term)
SUMMARY
In sum, it has taken centuries of semantics and positioning to move from the first identification that the Catholic Church is where Christ Jesus is and identified in their numerous cities to the distinguishing of the Roman Church from the Catholic Church and then to the Roman Catholic Church and finally to the recent self-identification that the Catholic Church is headquartered at Rome with those in communion with her head.
