That's weird to me because most Catholic people I know (Chicago is a very Catholic city) would identify themselves as "Catholic", not as "Christian". If you ask us "are you Christian", we'll say "yes", but it's not the word we use.
Maybe that's totally different for evangelicals or some other mainline denomination. I wouldn't know.
"Catholic" is just a Greek word that means "general, universal", derived from "kata holou" ("in accordance with the whole"). It's the opposite of a splintering off, though there is a viable argument that they splintered off of Orthodox Christianity (due originally to the filioque controversy, and arguably with broader differences relating e.g. to the worship of graven images, and the like).