Apologies for the alliteration, but it just came out that way. Pierogi, piroshky, pelmeni, and paczki (this is exhausting) are foods which are regularly confused with each other, what with the seemingly minor variations of dough and fillings seen among them. Between those variations, however, are distinct foods from different countries, though I'm pretty sure you can travel between them on a train rather quickly.
Let's establish some parameters before we proceed. Each type of dumpling and pastry mentioned above is actually the plural form in the original language. In Polish, pierogi is the plural of the singular pierog, a word that's rarely used because you'd look like an idiot eating a single pierog on a plate, as you would ordering just one piroshok, pelmen, or a lonely little paczek.
In the US, we often say "pierogies" or "piroshkies" as the plural, which is technically wrong, but if someone annoyingly corrects you on it, never invite them over again. If a person from Eastern Europe said "donutsies" instead of donuts, I wouldn't bat an eye.
Shaped like tubby crescent moons, pierogi have a soft exterior of unleavened dough that breaks through to an even softer filling of meat, fruit, or the esteemed potato-cheese. They're essentially a Polish brand of dumplings, and originated in the 13th century as a peasant food that gained popularity among the nobles (as I hope for my articles). You can boil, sauté, or fry them, but skip the cutlery and pick them up. It's like holding an edible stress ball.
Often confused with piroshky, the simplest way to remember the difference is this: Piroshky are kept in a display case and pierogi in a freezer, and while it's perfectly acceptable to dip a pierog in sour cream, doing so with a piroshok is grounds for imprisonment.
Hailing from Russia, piroshky are totally leavened hand-held pies which have way too many different spellings, including piroshki, pirozhki, pyrizhky, and "poopskies," as my nephew calls them. Their shapes are as varied as their fillings, which could be anything: cherries, potatoes, or your friend's keys.
Because various countries figured out how to stuff things into dough, it's nearly impossible to trace the base origin of all of these foods. The Italians have ravioli; the Japanese, gyoza; Americans, stuffed-crust pizza. Some theories suggest that they're all likely predated by jiaozi, a Chinese dumpling.
In any case, you'll definitely eat many more pelmeni than piroshky (we're moving along here), as they're much smaller Russian dumplings consisting of a filling wrapped in thin, unleavened dough. Is there a difference between the seemingly identical pelmeni and pierogi? You're damn right there is.
Pelmeni have raw fillings instead of pre-cooked, a much thinner dough shell, and are rarely sweet, traditionally featuring minced meat and spices. You call a pelmen a pierog, and you can expect a slap in the face. Best to keep your piroshky-hole shut.
Pazcki are the easiest to differentiate among this contrived selection of doughy goods, because they're basically doughnuts. I mean, they're not doughnuts if there are any Polish people reading this, but they're doughnuts (just better).
The dough is often richer and contains eggs, fats, and Spiritus vodka (yes!), which is then deep-fried and filled with jelly or cream. While eating them is intuitive, the pronunciation is not: "PAWNCH-kee" or "PUUNCH-kee" will get you by. Saying "PASS-key," as I have mistakenly for years, will not.
Well, there it is. Let's conclude this highly informative article with a question testing your knowledge: If you walk by a food cart, and they're selling a baked bready thing with exposed tubular meat and some mustard, what is that?
You guessed it! That's a hot dog. Thanks for paying attention.