It's a semantics thing. They're all "cartoons," in the sense that they're all animation, and most anime are derived from "comic" books of a sort.
Cartoons were originally short and rather satirical, the origin being the British satire magazine "Punch" contemporary to Dickens and based off of an Italian word for preliminary sketches. Animated cartoons followed the same idea, and while cartoon has been applied to the entire genre of animation, i still think that it would best be applied to theatrical shorts, or to half-length or third length (the 11 minute or 7 minute episodes that are put in pairs or trios to fill the half-hour programming slots on Cartoon Network and other channels), regardless of genre (from actual satire like MAD to screwball comedy like Spongebob Squarepants to some hybrid fantasy-comedy like Adventure Time), while full-length animated shows are just that, animated shows fitting in a genre.
Anime, then, falls under animation, and is usually in TV full-length format which would not merit the title of "cartoon," although it certainly is animation of just as much merit. Anime is just a shortened version of "Animeito" which, in turn, is just a Japan-ization of the word "Animate"
Monster Hunter: pissing me off since 2010.
