I would use battle mage to describe the same general character build as you: anything from a warrior who has a significant investment in offensive spells (just healing I'd consider more of a paladin, or something) to a mage that isn't afraid to pull out a melee weapon and get his hands dirty if opponents get close enough.
With regard to the Way of the Battle Mage skill, though, I would guess the term was chosen because there were two temporary boost spells for magic users, one defensive (Way of the Wise Wizard) and one offensive.
