There is 3 types of AOE in the game.
First is uncapped, single hit. Used by Lighting Missiles and other 1-shot type units, these strike all units in range for the damage listed.
Second is capped, single hit. Used by most AoE in the game, such as Grenade Launchers and Flak Turrets, these fire and then explode on the target ship, hitting up to certain number of targets nearby for the same damage. This type also comes in beam form on the zenith beam frigate, except instead of it hitting targets in range, it hits targets touched by its beam up to the cap on the targets in can hit.
Third is Electric Shuttles (and the units based off them). Each salvo from this ship has 200 'shots' and all shots hit a target in range, but only up to 5 times maximum per target. So if there are > 200 targets in range, 200 of the targets in range get hit once. If there are between 41 and 200 targets, each target gets hit multiple times until all 200 shots are used. If there are less then 40 ships in range, each ship in range gets hit by 5 shots and the rest of that salvo is wasted.
I suppose there are 4 actually, Plasma Siege Starships are weird enough they qualify as their own AoE type, but that ship description has how they work.