I figure that Paul was talking about the catholic church, and the current organization is the Catholic church. One is the universal community of believers, and the second is the commercial brand of one small part of that community.
cath·o·lic (kth-lk, kthlk)
adj.
1. Of broad or liberal scope; comprehensive: “The 100-odd pages of formulas and constants are surely the most catholic to be found” (Scientific American).
2. Including or concerning all humankind; universal: “what was of catholic rather than national interest” (J.A. Froude).
[Middle English catholik, universally accepted, from Old French catholique, from Latin catholicus, universal, from Greek katholikos, from katholou, in general : kat-, kata-, down, along, according to; see cata- + holou (from neuter genitive of holos, whole; see sol- in Indo-European roots).]
That is what Paul wrote about.
That is very nearly the opposite of what the Catholic Church is today.