Air superiority planes are fighters designed primarily to shoot down other any aircraft.
e.g. the F-22

planes are designed primarily to destroy incoming enemy bombers and reconnaissance/surveillance aircraft. They are fast, but carry fewer weapons. This type of aircraft is largely defunct today, and the last interceptor in service anywhere is the Mig-31:

Attack planes
are designed primarily to destroy ground targets like tanks, bunkers, or structures.
e.g. the A-10

Multi-role planes are designed to be competent at both the air superiority and attack roles.
e.g. the F/A-18