Alright, Chloe_01. This isn't rocket science, really. Pelmeni are typically much smaller, with a thinner dough, and almost *always* have a raw meat filling that cooks inside teh dumpling. They're usually served simple, maybe with sour cream or broth.
Pierogi, however, are larger, with a thicker dough, and the fillings are already cooked. Think potato and cheese, sauerkraut, or even sweet fruits. They're more versatile, used as a main dish, side, or even dessert. Big difference, trust me.