Animation is the process of making a series of frame-by-frame still images, when played sequentially, produces an animated motion picture. The medium used to produce those images could be anything, from hand-drawn cartoons, stop-motion puppets, computer graphics, to sand drawings on glass.
The term cartoon is overly generalized to encompass everything from editorial/satirical cartoons, comic strips, children's animated programs and feature films.
Because of it I don't use the term anymore.
Here's how the dictionary defines cartoon:
a simple drawing showing the features of its subjects in a humorously exaggerated way, esp. a satirical one in a newspaper or magazine.
a motion picture using animation techniques to photograph a sequence of drawings rather than real people or objects.
When I think of the word cartoon, I think of the first definition, which defines editorial cartoons such as this:
We're not interested in that, so let's set those aside and just focus on the second definition, emphasizing the part about the "sequence of drawings".
An animated cartoon involves flat, hand-drawn artwork.
Most people would agree that the Warner Brothers' hand-drawn short film Hair-Raising Hare fits the classic definition of a cartoon:
Is the computer-generated short film Oktapodi from the Gobelins school a cartoon? If you ask me personally, I will say no, because it does not fit neither mine nor the dictionary definition of it being hand-drawn.
If someone were to mention Walt Disney's classic Sleeping Beauty, I would call this an animated movie. It doesn't fit my own definition of a cartoon because of its long, 76-minute running time. It does fit the dictionary definition of a cartoon, so if you want to call it that, fine by me.
Some of the confusion clouding the popular definition of cartoon may arise out of its association in American culture with animated films created for children's consumption. I refer to the "cartoons are for kids" mentality. A parent would assume that just because a film is animated, therefore it must be ok for their toddler to watch.
Marjane Satrapi's Oscar-nominated Persepolis, like Sleeping Beauty, is a hand-drawn animated film that fits the definition of a cartoon, but would your kid want to sit through this film about a girl growing up during the Iranian Revolution? If adults make up the target audience, would you still consider this a cartoon, or would you prefer to call this an animated film?