@lnx all 4 of my classes (adventurer, rogue, warrior, mage) have a basic Attack option. it goes off of the attacker's ATK stat and the targets's physical defense, which can be affected by any number of things but mostly weapons and armor.
Rogues, Warriors, and Adventurers have 4 skill slots. You can buy skills in shops and swap them out at any time outside of battle. Most of them are based on physical attack as well, but the Rogue does have a spell that will analyze an enemy's stats.
Mages have 6 skill slots, because they have way more of them to choose from and 4 felt a bit too cramped for them. All of their skills go off of their magic stats.
In addition to the above, the luck stat is always taken into account, so the more lucky your character is the more damage they will deal and that gets applied after everything else. Rogues are the most lucky and warriors are the least.