That's because the class is a gameplay mechanic more than anything, as far as I can tell from the stories. Yeah, obviously the medics are distinguished, and the people using arts primarily have that noted, but we have to recall that Nearl is both a defender and a guard simultaneously due to the alters, and Shining is a combat monster despite being a medic (and then there's the story stuff Saria does, which has way more punching).

Just focus on your abilities rather than worrying too much about the game divisions. xD