> All of the three main branches of Christianity in the East (Eastern Orthodox Church, Oriental Orthodox Church and Church of the East) had always identified themselves as Catholic in accordance with Apostolic traditions and the Nicene Creed. Anglicans, Lutherans, and some Methodists also believe that their churches are "Catholic" in the sense that they too are in continuity with the original universal church founded by the Apostles. However, each church defines the scope of the "Catholic Church" differently. For instance, the Roman Catholic, Eastern Orthodox, Oriental Orthodox churches, and Church of the East, each maintain that their own denomination is identical with the original universal church, from which all other denominations broke away.

- https://en.wikipedia.org/wiki/Catholic_(term)

Greek Orthodox are "Catholic" but they are not "Roman Catholic".

In Christian dogma terms, sure, but if you call an (edit) Orthodox Greek Catholic, they will quite disagree.

Unless they are a Greek Catholic.

https://en.wikipedia.org/wiki/Greek_Catholic_Church

Or Roman Catholic, yes.

Sounds like the only visual analogy is the branching of a broccoli head, or something equally dense and fractal.

The tree of life works better, there were many branches even earlier that died off and the ones that survive did so through evolutionary pressure. The ones that required circumcision for instance weren't great at attracting converts.

I'll take your word for it, I've been to Divine Liturgy exactly once.

Do Orthodox folks not use the term "Catholic" for themselves? I just don't know very many.

No, it's "Orthodox Christian" and "Catholic Christian", to differentiate.

Conversely, the Catholics I know prefer (if they have a preference, many don't) the bare term "Catholic" rather than "Catholic Christian". This is likely because I live in the US.

Now that you mention it, I've only heard them called "Catholics" here as well, not "Catholic Christian", so it's "Orthodox" or "Orthodox Christian" and "Catholic", you're right.