The true church is not a name, it is comprised of all born-again believers in Jesus Christ. She is called the “bride of Christ.”
The first, original Christians were the “followers of the Christos”. Now there were those that branched off. But the term “catholic” w/a ‘small c’ meant ‘universal’. Then there were the different ‘rites’ or branches.
There were the Latin-Rite, (or Roman Catholic, Church of Rome) the Coptic-Rite (Egyptian), the Greek-Rite, Slavic (Eastern-Rite or Russian), Armenian-Rite, the Chaldeon-Rite(not sure of spelling on that), which is mostly located in Iraq, I think, and the Syrian-Rite. Many of those ‘rites’ were/are under the Church of Rome now, but keep their identity and liturgies, cultures, etc... Now if I don’t have the names right, or missed one, someone please let me know.
So in a sense, those could all claim to be ‘catholic’ or ‘universal’! There were all those branches. Then there were more: (Anglican Rite), and the Orthodox rites that came after the ‘Schism’. Then of course, were the various Protestant branches.