Your testimony is not credible.
Of course the words”denomination”and “religion” are fluid terms of convenience. Barth said, I am told, the Xtianity is not a “religion,” and neither Byzantines nor Catholics consider their communions to be “denominations.”
As near as I can say it in this medium, the Catholic Church holds that there is one Church only and that all who are baptized properly are members of it, and maybe some others too. “Catholics” as designation of a group denotes those in full communion with the Holy See. But that group does not exhaust the membership of the Church.
In any case, it’s a waste of time to take these terms and build a criticism of Catholic thought, because they are used in a restricted and sometimes even confusing way.
That’s how I see it anyway.