It's a type of dumpling that comes from Georgia(country). Personally, I haven't been to authentic restaurants, but I've tried a fair share of frozen ones, and a few from the deliveries, and I must say I like them a lot more than any kind of pelmeni(Russian dumplings).
I don't know how to describe the taste. It tastes a lot like many other dumplings with meat. The difference is mostly in spices and the fact that the tastiest part of khinkali is a broth\meat juice.
Americans somehow didn't get the memo that dumplings were supposed to be stuffed so we have stuff like chicken n' dumplings. You know what? I'll fix that by sealing the chicken and soup from chicken n' dumplings and stuffing them in dumpling dough as they should be. Though I now also want to try Khinkali.
The most important part of ordinary khinkali is that there should be minced meat, spices, and, I'm sorry, I don't know how exactly this happens, but once you boil it, enough juice\broth appears in the dumpling. That's why it looks that way. You eat it with your hands. You turn them upside down, bite into the bottom(large) part and drink all the juice.
As for chicken and dumplings, I think the problem here is that you name all dumplings as dumplings. Like, I don't even remember if we have a literal translation of the word dumpling in Russian. We call every variation by its name.
Truth about the naming. As a cooking fanatic, I can't understand why people in America don't care to be specific about certain foods.it makes it much more difficult to find where said specific food is sold.
It's because I can't find a proper translation of Ukrainian Halušky. Ukrainian Halušky are bits of boiled dough, a type of dumpling without any filling. Sometimes you eat them as is, and sometimes you make soup with them.
That's fairly similar. However, Chicken n' dumplings are made by starting a roux and then adding chicken broth, vegetables, milk, chicken broth, and spices to make gravy or sauce. then you add in the chicken and the dumpling dough into the mixture and cook till the soup is done and serve. so it's more of a soup than a meal you can eat with your hands.