Just to split hairs:
When a pump sucks air, that's aeration. The flow leaving the pump will be laden with bubbles that will persist until there is a place in the flow path where they can separate.
Aeration can be harsh because the pump can overspeed when it loses its prime, and this can damage the drive coupling. Also, developed head goes 'way down while there is entrained air because of the lower density of the charge in the impeller. This is a prime justification for a check valve on the outlet of the pump. If the pump sucks air, loses prime, and the developed pressure falls off, then the pressurized fluid downstream will probably rush backwards into the pump. A big slug of liquid flowing into an overspeeding impeller can be really shocky to the drive coupling, shaft, keys, etc.
WHen a pump is flowing single-phase liquid and the inlet pressure decreases to below the NPSH number, the water in the impeller flashes to steam. Then the steam bubbles collapse on the front side of the next impeller blade. That is Cavitation. Cavitation causes surface damage to the impeller and housing, but the fluid leaving the pump is all liquid (the steam bubbles collapse and all the fluid returns to liquid phase). It sounds like the pump is pumping gravel.