No it doesn't, anime is a specific genre of animation (like JRPGs are just a genre of RPG). Manga is just the Japanese term for comics.
Er... no. "Anime" is short for "animeeshyon" (アニメーション) which is the Japanese spelling of "animation" and according to online dictionary jisho.org translates to:
1: animation;
2: animated film; animated cartoon
or in the case of "anime":
1: animated film; animated cartoon; anime (when referring to Japanese cartoons)
So, just like "manga" it is a general term for anything that we label "animation" or "cartoon" in Japan itself, but becomes a term that specifically refers to the country of origin when being used outside of Japan. Oh, and I found
this for the sake of amusement.
and self-deprecation since I use a Japanese honorific in my Twitter handle