Anime and cartoons are certainly both words in the west accustomed to different genres (they may mean the mean the same in Japan, but mean they are different in the west, ala comics and manga). Anime is mostly defined as animated series made in Japan (be it Pokemon, Hellsing, or Panty & Stocking with Garterbelt (which has a more western-style)) and cartoon has a mostly defined style as being for western children (Tom & Jerry, Dexter's Laboratory, etc.).
Obviously, each crosses over in terms of terms of target audience, and even in style, but for the most part they can be differentiated.