Manga is Japanese for comic? Yes.
Anime is Japanese for animation? Yes.
Is a tomato a fruit? Yes.
Would you put a tomato in a fruit salad? No.
Yes, an anime is just Japanese for animation, and yes, a manga is just Japanese for manga, but there's still a significant difference between the two. Just like how you wouldn't put a tomato in a fruit salad, you wouldn't call Spongebob Squarepants or the Simpsons an "anime", and you wouldn't call the original Superman or Batman comics a "manga".
A manga is a comic, but a comic is not necessarily a manga.
An anime is a cartoon animation, but a cartoon animation is not necessarily an anime.