What are the similarities and differences between prokaryotic and eukaryotic cells?

The terms both refer to cells that make up living things, and the main difference is in the definition of both--prokaryote means a cell without a nucleus, and eukaryote means a cell with a nucleus ("eu" means true.)

Prokaryotes are unicellular organisms such as bacteria. Their DNA is not contained within a nucleus, so duplication of DNA takes place in the cytoplasm. Eukaryotic cells make up multicellular plants and animals; there are also some that are unicellular organisms. Their DNA is contained within a separate area, the nucleus. DNA replication takes place there, and RNA leaves the nucleus, with protein synthesis taking place in the cytoplasm.

Prokaryotes are, in general, simpler than eukaryotes; eukaryotes have more separation of function.