Easy, Medium, Hard. What changes depending on this selection? I know they influence the goals, especially the bonus/secret goals. And I'm pretty sure they influence scoring.

Anything else? Can't just be bonus goals, because some missions have exactly the same goals regardless of difficultly level. Not damage, as far as I can tell, nor ship performance... Maybe warhead speed, like in X-Wing Alliance? Enemy AI? Enemy composition?

I suspect that with a game this old (and I did play it back in the day), there should be a precise list compiled somewhere. But I haven't been able to find one.

They change the AI balance, on easy your wingmen have better AI than the enemy, on hard is viceversa and on medium they are about the same.
The trouble is that hard can really break the missions because your wingmen on hard are DUMB and often get shredded at the moment they come into weapons range of the enemy fighters.
Depending on the game (and sometimes on the specific mission) they also allow or disallow the destruction of turbolasers, missile launchers or shield generators when the shields of the target are still up.
XvT for example allow to do so only on easy while XWA allows it on easy and medium but not on hard.

If I remember correctly how the mission editors worked, you could also flag some flight wings (both enemy and allies) to come out only at certain difficulty levels