While all ArcheAge mounts may be used in combat, battle pets are significantly stronger. Both pet types have their own character screens and equipment, but battle pets feature more active skills. You'll also need to be level 25 to obtain the battle pet quest (as opposed to level 5 for basic mounts).
Also like mounts, battle pets have their own levels which are advanced through hunting mobs (gathering, crafting, and quest turn-in XP does not affect either pet type). Finally, battle pets can die and will lose XP when they do. Head to ArcheAge Source for a lengthy system breakdown, and check out the baby wolf video after the cut.
[Thanks to Dengar for the tip!]