Prokaryotic cells do not have membrane bound organelles. However, they have DNA in their cytosol as well as ribosomes. They can have pili as well as flagella. Examples are bacteria and archaea. Eukaryotic cells are found in organisms including--fungi, protists, animals and plants. These contain organelles that carry out different functions. They have a nucleus, nucleolus, cytoplasm, mitochondria, rough and smooth endoplasmic reticulum, golgi apparatus, lysosomes, cell membrane. In plants and fungi, and some protists, a cell wall is present. Chloroplasts are found in plants and algae cells. Centrioles are found in animal cells. Basically, eukaryotic cells have more components that perform specialized life functions.
There are two potential answers to this question. At the most broad definition of a cell, the two major types of cells are prokaryotic and eukaryotic cells. Prokaryotic cells are simpler cells that do not contain a nucleus or other membrane bound organelles. All of their components are simply contained in the cytoplasm. Most of these cells are single celled creatures like bacteria. Eukaryotic cells are more complex and contain a nucleus and organelles like mitochondria, ribosomes, Golgi complex, etc. These cells make up complex, multicellular creatures like animals.
Within eukaryotic cells of multicellular organisms, there are also two different types of cells. Sexual cells are gametes like ovum and sperm that combine during sexual reproduction to create a new organism. Somatic cells are the other type of cells. These literally consist of every other type of cell that is not a sexual cell, like a red blood cell.