Based on my opinion on what you can get out of martial arts (i.e. what type of goals someone may have for taking the arts):
- Combat & Self Defense
- Sport & Competition
- Wellness
- Expression
The first two should be pretty obvious what I'm talking about, so let's move onto the others. Wellness could mean physical conditioning, but it can also mean balance, flexibility, emotional wellness (it's better than going to the bar after a bad day at work), memory (especially if your art has forms), and coordination.
Then there's expression, which could be demonstrations, tricking, integration with dance or gymnastics, or simply to be a stunt man for movies and shows.
So the first idea, Combat & Self Defense, I split into Martial Art and Martial Science. (Notice both are "martial"). The other three goals fit into the three obvious archetypes. Why "art" and "science"? Because I feel the forms are more artsy.