Larry, based on my experience living in a Greek-American neighborhood in NYC (Astoria, Queens), where we ate a LOT of Greek food, I think there are several answers to this question but not one single canonical form.
Greek yogurt, depending on whose menu you're looking at, may be:
1) Rich, creamy, whole-milk yogurt, no different than any other fresh whole-milk yogurt.
2) The same, allowed to sit in a cheesecloth bag overnight so much of the liquid runs out, leaving a thicker product akin to farmer cheese or <i>fromage blanc</i>. Again, no different from other ethnic yogurts except that you eat it in a Greek restaurant.
3) Either of the above, served as a dessert garnished with almonds and drizzled with honey. That's Greek.
That's my story, anyway, but I'm telling it from Greek dining experience, not from books or Google.