I don't believe there is any industry standard term for these parts; they're often used interchangeably. However in general:
Airbrakes and speedbrakes are interchangeable terms; just large reinforced panels which can be extended out from the aerodynamic envelope, creating a lot of parasite drag.
Spoilers and Lift Dumpers are, again, interchangeable terms. These are just speed brakes mounted on the upper wing surfaces, in general, about 1/2 to 2/3 the length of the chord line. In addition to creating parasite drag, they induce flow separation over the top of the wing and, as mentioned above, greatly increasing induced drag in the process as the lift is 'dumped' off during deployment. Large transports will use spoilers to increase braking effectiveness and decrease the length of the landing roll.
Another function of spoilers is roll authority, particularly in fly by wire aircraft, but sometimes seen in other types of mechanically controlled aircraft e.g MU-2, TBM, etc. They will be used in conjunction with other control surfaces such as ailerons, all-moving tailplanes, etc.