The first assumption seems valid - a fighter group in a fleet would follow its task force strategy. Launched fighters I would guess follow their design type strategy, but I wouldn't be surprised if they followed the strategy of the task force that the carrier was in either.
Thank you! So, the tactic selected when designing fighters is key, if they are to be launched from carriers. And, you can build different fighters with tactics for different roles (engage enemy fighters, attack unarmed ships, etc.).