Eh, it's hard to determine the label for animation. If you want to get literal, you'll end up involving a bunch of films that seem out of place or have tons of "BUT WHAT ABOUT" responses.
If you say it can only be drawn, made from scratch, digitally made on a program, etc. (2D films, CGI films), then the arguement of stop-motion would appear.
I typically like to refer to animation as a 2D or CGI product. Stop-motion I would either refer to as stop-motion or animation, like if I were telling someone what Wallace and Gromit is, I would say "It's stop-motion animation" instead of just "It's animation". When talking about Polar Express or Beowulf, I would say it's motion-captured. With Avatar, I say it's a mix; a live-action movie with motion capture used as a special effect.
I think referring to all of those as just animation is too broad, especially since they're apples and oranges. Imagine a movie like Avatar beating Toy Story 3 or something for "Best Animated Film", the animation techniques are so vastly different that having them compete would be silly (As well as many fans of the movie feeling copped-out if the other movie won).
I would consider Roger Rabbit an animated film more than Avatar.
I do think the job label for all of those techniques would be "animators", since they are all doing frame-by-frame work, but the product itself is something very specific.
EDIT: As for the "Avatar is so heavily mo-capped" thing, many Superheroes are so heavily placed under special effects, but they are still considered actors and not animation.