The term anime, while created directly in relation to Japan's animation industry being on the rise in the 1970's. In truth, there's no special reason behind this except the fact it's a shorter, faster way to say animation.
Anime, or アニメ(A–Ni–Me), would be アニメーション (A–Ni–Me–Sho–N), longer, and rather unnecessary when the first is just as understandable and recognizable. It was a term created for its ease, quite like how in English, people will say ASAP instead of 'as soon as possible.' You can use the full version but usually there's no need to do so.
When traveling to different regions there's usually a style that's favored. Be it with colors, food, or art. Art in particular stands out. Italian art contains a lot of frescos, paintings done on wet plaster, while European art contains a lot of oil paintings. With time, artwork and their techniques evolved, till animation became another form or art.
There are different types of art in the world, belonging to different places, different people, but that does not change the fact that they are art. Much like with animation, they are made in different places by different people and called different things, but they are still considered animation.