FDM aka FFF: extrudes out of nozzle like frosting on a cake. Usually less expensive than other types of printing and the parts are more durable but the finish is not as good and layers are visible.

Objet: Works like a regular printer depositing a small layer of powder and then fusing that powder with a lazer. Great for precise parts with a beautiful finish but not very durable.

SLA: Very detailed, light cured resin.

Jetting: very high detail and high resolution.

LOM: Laminated Objet: Prints in Paper.

SLS: Selective Lazer Sintering. Laser crisps powder (mostly industrial) can print metal, used for medical stuff.

3D Doddler: used by had to close seems, etc.  like a pen