I did some digging and found that Dolma (Turkish name for vine leaf wraps we have here in Greece as well with the same name), Mahshi and Γεμιστά (rice stuffed vegetables) are etymologically the same word "stuffed / to stuff-fill with".

Due to the proximity of Greece, Türkiye, Egypt etc it makes sense that we share that dish with basically the same name translated in each language.

It's usually served with an egg-lemon-broth sauce. Sometimes thickened a bit with some corn starch. It's very mild tasting, not as "eggy" as you'd expect. Apparently they're known as "Greek cabbage rolls" if you wanna get a recipe

That's another dish. In Greek we call them by their Turkish name "Ντολμαδάκια" or "Ντολμάδες" for the grape leaf ones (the Turkish word is Dolma for something stuffed)

The cabbage ones are "Λαχανοντολμάδες", with the word "Λάχανο" added in front which means cabbage, so "cabbage Dolma".

Essentially the cabbage ones are named as a variation of the grape leaf recipe.

Their main difference is the grape leaf ones are mostly served "dry", more like sushi.