The church we call ‘Catholic’ today is the church that Christ founded…it wasn’t formally called the Catholic Church at first because there was no need to clarify. The Church was the Church was the Church.
In response to the various errors, schisms, splinter groups, etc. that began springing up early in the history, calling the ‘official’ Church ‘Catholic’ became more and more the norm to emphasize that it was the universal Church and the others were not. This became even more prevalent and ‘official’ following the Great Schism and the Protestant Reformation, to continue emphasizing that this is the Church founded by Christ.
Differentiation between the ‘catholic’ church (the original church founded by Christ) and the ‘Catholic’ church as we know it today is false differentiation. They are the same thing, evolved and grown over the intervening millennia. Other churches, except perhaps the Orthodox, cannot claim this kind of direct succession from Jesus and the Apostles.
God bless you.