There are many different types of landing craft, and many of them were used in the amphibious assault on Normandy. There were even some specially modified craft designed to carry guns for extra support, such as the Landing Craft Gun, the Landing Craft Rocket, and the Landing Craft Assault. Here is a list of several different types.
LBW: Landing Barge.
LCA: Landing Craft, Assault.
LCE: Landing Craft, Equipment.
LCF: Landing Craft, Flak.
LCI: Landing Craft, Infantry.
LCI (L): Landing Craft, Infantry (Light).
LCOCU: Landing Craft, Obstacle Clearance Unit.
LCM: Landing Craft, Medium.
LCR: Landing Craft, Rockets.
LCT: Landing Craft, Tank.
LCT (A): Landing Craft Transport, Assault.
LCT (R): Landing Craft Transport, Rocket.
LCV: Landing Craft, Vehicle.
LCVP: Landing Craft, Vehicle and Personnel.
LO: Liaison Officer.
LSI: Landing Ship, Infantry.
LST: Landing Ship, Tank.