People have been calling random American-style or generic Western-style cartoons "anime" around me, lately, and that really pisses me the hell off. "Anime" would be that Japanese style of cartoon, and NOT the American style. They are very different, and I can tell them apart. I may not be able to tell a UK cartoon from a US cartoon, and I may not be able to tell the difference between a Western artist drawing anime style and an Eastern artist drawing anime style, but I can tell the difference between a Western-style cartoon and anime. They are NOT the same.
"Cartoon" is the generic class. "Anime" is a specific subset. I am not entirely certain of the difference between anime and manga (one is animated and one is drawn, I think?) It's like calling all computers Dells, or calling all cars Fords. It is wrong, so stop the fuck doing it!