Can someone please explain to me the difference between Offense Mods and Crit Dmg?

short answer - offense mods improve base damage, crit damage mods only increase damage when you get a critical hit

longer answer - offense mods improve every hit that you make and are taken into account before the crit damage bonus. Crit damage mods only increase the amount of damage you do when you score a critical hit. If you score a critical hit a crit damage set is better than an offense set. If you don't score a critical hit then an offense set is better. Because you need to crit to get the bonus from crit damage mods they are usually paired with a crit chance set.