Eukaryotic cells are distinct from prokaryotic cells primarily through the presence of a nucleus and membrane-bound organelles in eukaryotes, while prokaryotes lack these structures. Eukaryotic cells include organisms like animals, plants, and fungi, whereas prokaryotes are mainly represented by bacteria and archaea. The complexity of eukaryotic cells allows for compartmentalization of cellular processes, leading to greater functionality and specialization compared to the simpler, more primitive structure of prokaryotic cells.