This question requires some historical background that, without, would be difficult to accurately consider.
First-century Christianity did not require additional reference terms, since there were no other forms of it.
The earliest "Christians" were all Jews, no gentile could then become a Christian, since the promise given to Abraham, for an "inheritance"- a "kingdom"- applied strictly to the line Abraham.- Genesis 22:18
(Galatians 3:29, Isaiah 2:1-3, Daniel 7:22 and 27, Luke 22:28-30, 12;32, Hebrews 12:28, Revelations 1:6)
Only after the "inheritance" had been sufficiently offered to all Jews who were willing to accept it, could the "inheritance" be opened to gentiles who where willing to fulfill its obligations.- Romans 8:12,17
And this took place, only because of disobedience and stubborn attitudes that prevented the entire Jewish nation, from providing the entire number of "Christians"- disciples of Christ, as they were to become known- from fulfilling the promise, or "inheritance".
No, the "inheritance' did not concern individual salvation, but a leadership role with the "Messiah", in governing and bringing deliverance and salvation about.
This was what was at the center of early-Christian activity- the "inheritance", in connection with the promised "messiah". Not to be fulfilled through earthly means, but through literal, spiritual intervention, as Revelations Chapter 21 explains.
The "inheritance"- which involved a leading role in delivering the peoples of the "nations" from distress (Revelations 21:1-2)- is limited in number, as any responsible assignment, is.- Revelation 7:4
The Bible describes those willingly accepting this assignment as those who "were bought from among mankind as firstfruits to God and to the Lamb."- Rev.14:4
God selected the number, for his own reasons, humans have nothing to do with that decision.
Gentiles were, of course, not well educated in these matters, so the Jewish Christians- who themselves, had to readjust some of their views- discovered that it was necessary to teach the influx of gentiles, the basic "things of God" that they were not yet equipped to understand. Human pride, on both sides, had to be set aside and dismissed, to achieve this.
These early-Christians all shared a Judaic heritage, either by lineage or by adoption.
They might even be referred to as "Judaic Christians", in order to distinguish them from other religious elements, that were to later spring up.
Following the death of the apostles, more and more Gentiles, who possessed spiritsitic religious backgrounds, began filtering into Christianity. (The Catholic Church did not yet exist.)
The unchristian views that many- not all, but many- would begin to promote, would have a serous effect on the Judaic Christian community. The Apostles were aware this crises was coming:
"Let no one lead you astray in any way, because it (the "end") will not come unless the apostasy comes first and the man of lawlessness gets revealed".- 2 Thessalonians 2:3, also compare Luke 20:24
Judaic Christians were neither Catholic nor Protestant.
Like their faithful ancestors, Judaic Christians worshiped "Jehovah" as "heavenly father" and "God", and were dedicated to Jesus as a "mediator" between man and God (1 Timothy 2:5), and as messianic "king" and head of the Christian Congregation of "holy ones" (Daniel 7;22, 27-28), who inherited the promise of sharing in a leading role that would inevitably result in deliverance, salvation and extensive blessings for mankind.
In contrast, Christendom worships a trinity godhead, which may be somewhat more complex than the popular Roman/Grekko/Egyptian/ Babylonian pantheon trinities, that flourished in the ancient gentile world, along with mother/child worship. Christendom also emphasizes personal salvation, rather than deliverance by means of the "kingdom" and the "inheritance".
Christians from the Judaic world believed and taught that man is mortal and dies. And that mankind's hope rests in the "resurrection", referred to at Acts 24:15. Christendom teaches that man is immortal, never truly dies, but transfers to heaven or hell, at death.
Christians used fire to denote total, complete destruction (sometimes tormenting shame), but never projected the existence of an abode where humans burn forever.
Judaic Christians were organized on the basis of an "ekklesia" (Greek), awkwardly translated into the english term "congregation", which involved significant differences in organization and character, that set it apart from the laity-clerical arrangement that was intrinsic to the Catholic concept of "church".
Thus it is accurate to refer to the Catholic Church as the "first church". And its authorized translations of the Bible, should not be considered free of suggestions that reflect its teachings; this is the natural result of the duplication of Bible manuscripts into suitable translations for use throughout Christendom. Whether they agree with what was put to text by Judaic writers of scripture, is another matter.
Judaic Christians were non-political, non-commercial, and engaged in teaching, rather than concerned with 'Christianizing' nations.
Christendom is highly-political and highly-commercialized, and has actively been engaged in the mass "Christianizing' of nations, since its birth, in 4th-century Europe.
