This has come up in our group a number of times. Some action cards say remove a ship, is a fighter a ship for these purposes?

Assume a fighter counts unless it says otherwise, the rules seem to be careful to say when a fighter doesn't count as a ship.

Aye, the rules usually say something like "non-fighters" or "excluding fighters" when they mean for it not to apply to fighters.

Yes, this makes the 1VP-objective "destroyed 3 ships in a single combat this round" rather easy.

Spot a Carrier, and hunt it down with a few Destroyers.