Looking at the original meanings of the words: catholic means simply "universal" (as in "in charge of the Universe") and orthodox means "having the right belief" (right as opposed to wrong, not to the left). Only the later use of the words in some specific parts of the world gave some new (today often automatically assumed) meanings (created in the lands of their old opponents). The "orthodox" churches are proud to have "the right belief" and they don't think about the newer less positive meanings. They also consider themselves, of course "universal" because they used the very term before the schism too.

Unsurprisingly both modern "Catholics" and "Orthodox" churches claim that their influence is "worldwide" and that they are right.