There is also a peroshie which uses a yeast dough and are either baked or deep fried. They are filled like piroghi (vereneky) and look like them but are a golden brown from the cooking (not boiled process). I haven't made any yet but you reminded that they are on my to do list.
I make Pierogis several times a year and I have found a great way to make them that is simple. They are called poor mans pierogi. Get yourself some won ton wraps. Make your pierogi filling and put a dob of it on the won ton. Using your finger dappen the edges of the won ton with water and then fold over or fold in anyway you want. Fry in butter until brown. they also freeze well. Freeze on cookie sheet and when frozen pack in bags. We love the filling of mashed potato, spiced sausage and cheese. Just make sure the mashed potatoes are NOT to moist. Better to make them drier.