Actually, I'm curious about that. I understand that "anime" in japan is a blanket term for all kinds of drawn animation, including western-style - so the meaning is more similar to US "cartoon" or german "Zeichentrick".
But given that the distinct japanese style of animation and storytelling (what the west knows as "anime") has spawned a whole industry and subculture and has become part of japan's image in the world, it would seem to me to be too important to not give it a distinct name. So I wonder, is there a different term in japanese for it?
A weird detail is the Chinese transliteration of "karaoke":卡拉OK. It starts out with two Chinese characters pronounced "ka" and "la", and then tacks on the English "OK": ka-la-OK. So the English word "orchestra" turned into "OK" after two transliterations.