Actually "anime," while being a Japanese word, doesn't distinctly refer to Japanese animation itself. It's simply a word that refers to all motion animation.

The term, however, is used in a different context outside of Japan to indicate a certain style of animation that is prevalent in Japan (though also extends to other parts of Asia).

While I was content with just leaving it as "Japanese animation" for the sake of simplicity, if we're going to get into a pedantic discussion of the word's meaning and usage, I feel that it should at least be pointed out that there's a non-marginal difference between the word's actual meaning and its context when adopted by foreigners ("foreigners," in this case, referring to those who are foreign to Japan).