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