Do enemies have weaknesses to certain attacks?

Does it matter if I kill a monster with a sword or magic attack? Will one do more than another? Also what about damage from orbs?

Some enemies have armor against physical damage, making magic damage work better against them. Others resist magic better than physical damage.

Also, you can upgrade your weapon and your staff which increases the damage they do. So, depending on how you upgraded your weapon and staff, and what defenses are stronger on your opponent, it can make a great deal of difference whether you attack with your weapon or magic.

Orbs do magical damage.

Axes do physical damage.