So, I think it was clarified for me like this...
When Combat is specified = Fight + Weapons
When Fight is specified = Just Fight Skill
If by this you mean the same thing Professor said, then ok. Otherwise, I think you might be slightly off course.
There are two type of bonuses, Combat bonuses and Fight bonuses. All Fight bonuses are also Combat bonuses, but Combat bonuses are not Fight bonuses.
Therefore, in Combat, you gain all + Combat and all + Fight modifiers. If you're maing a Fight skill check outside of combat, you only get + Fight modifiers. This is not quite the same as saying "Combat = Fight + Weapons" because it is possible that some weapons may provide a + Fight bonus, which would apply to Fight checks equally well.
Combat = Fight Skill + Fight Modifers + Combat Modifiers
Fight Check = Fight Skill + Fight Modifiers