Check out this page from Wikipedia. Dolma - Wikipedia, the free encyclopedia
It gives a nice overview of the variations.
If you scroll down about half way down the page, you'll see a section starting, "In Armenian cuisine..." This gives a good description of the hot dish. In our Armenian circles we referred to the stuffed rolled cabbage and grape leves as sarma and the stuffed vegetables (peppers, tomatoes, zucchini) as dolma.
Further down the page, in the section beginning, "In Turkey...", there is reference to "yalancı dolma". This is a cold appetizer served as part of a meze course prior to the main meal. We call this yalangi.
The real message you get from this page should be that dishes are not bound by political borders. A stuffed grape (or cabbage) leaf is a staple in many cultures across thousands of miles on several continents. It doesn't belong to anyone culture. There are variations based on local preferences.