Easy gives a 20% bonus on all skills, normal has no bonuses and no penalties, and hard gives a 10% penalty on all skills. That's all there is about game difficulty, if I recall correctly. There may be some other stuff, but this is probably most important.
About combat difficulty: as it is set to be more difficult, the enemies will use more sophisticated tactics, like called shots, attacking those who attack them, attacking weaker members of your party, etc.