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.
The associated list page is worth reading too, if only to see how much of the meaning you can guess just by looking at the first 3 columns of that table: