Both eukaryotes and prokaryotes are types of living cell. The types of cell you normally consider in the animal body are eukaryotes. They have a cell membrane around the outside, with a nuceus in its own membrane inside. There are also other membrane-bound organelles such as mitochondria, endoplasmic reticulum and vesicles. Eukaryotes are differentiated cells, and their DNA is held exclusively in the nucleus. Prokaryotes are things like bacteria, and they have both a cell membrane and a cell wall. There is no nuclear membrane, instead their DNA is looped freely in the cytoplasm, although sometime there is extra nuclear material wrapped in plasmids. Prokaryotes don't generally have mitochondria, they can have other extra features instead, eg a flagellum (tail). Also, the ribosomes of prokaryotes are a lot smaller, as well as the whole cell being smaller.