Yeah, basically. Basic -> Advanced -> Elite is the terminology we use in-game. Each time the unit levels up (which is automatic), that unit gains +1 in its primary attack (hack, pierce, crush, etc.) and +1 in its primary armour type. Super Units, like Spartiates and Anusiya, don't need to "level up" because they are already Elite soldiers. And as soldiers get better at fighting, they get worse at econ. XP is accrued through kills and amount of time the unit lives. So, you are encouraged not to waste your men in futile actions. You are rewarded for giving your men experience and victory.