To steal mercilessly from Wikipedia: The most important difference between pelmeni, varenyky, and pierogi is the thickness of the dough shell—in pelmeni and va

To steal mercilessly from Wikipedia: The most important difference between pelmeni, varenyky, and pierogi is the thickness of the dough shell—in pelmeni and vareniki this is as thin as possible, and the proportion of filling to dough is usually higher. Pelmeni are never served with a sweet filling, which distinguishes them from vareniki and Polish pierogi, which sometimes are. Also, the fillings in pelmeni are usually raw, while the fillings of vareniki and pierogi are typically precooked. Those distinctions seem about right in my experience, and I eat all three fairly often, since I go to a lot of cultural festivals.