Tell them that there's a difference between Japanese animation and Japanese-styled comics, which are known as anime and manga, and western-style cartoons, which are normally for children (with the exception of things like Family Guy and South Park), whereas a lot of anime can be for teens and adults (although there are anime for children). Anime normally has a certain style for drawing (big eyes, small noses and mouths, small pointed chins) whereas cartoons normally are just drawn in whatever style the creator feels like.
Also, it would help to show them some fact videos about anime, which would probably make explaining any further a little easier.