For the most part, yes.
It definitely is an attempt to distinguish between the “Roman” (or Latin) and the “Greek” liturgical traditions, since we like to put everything in nice little boxes in order to understand them better. But it should be mentioned that the Greeks (or Greek speaking Hellenes) throughout the Middle east considered themselves Romans for most of the time when this liturgical tradition was in formation. They were very proud of this, and could have called themselves Roman and Catholic with accuracy.
It was the East Roman empire and it’s own Great Church of Hagia Sophia which set the standard for worship using the liturgy of St John Chrysostom/St Basil. Then Saint Photios launched the missions of Ss Cyril and Methodios which carried this into central and eastern Europe. Naturally, Greek ethnicity has little to do with it and it is not unique to the Greek state, and most of the believers do not use the Greek language in worship. It pretty much refers to the East Roman liturgical tradition of Hagia Sophia, commonly thought of as ‘Greek’ to modern western people. The alternative term, Byzantine, is also a western label, which the East Romans and Greeks do not seem to have ever used to describe themselves.
I have seen it referred to the"Methodian Rite" as used in central Europe in some accounts.
I believe it was Empress Maria Theresa who first popularized the term ‘Greek Catholic’, referring in her case to distinguish converts from among her ‘Greek Orthodox’ subjects who were allowed to keep their ritual traditions.
For what it’s worth, Orthodox also still use the term.