おなか is very common word to say "stomach" or "belly," but is not a name of an organ. For Example;
おなかが すいた。 I'm hungry.
おなかが いたい。 I have a stomachache. (NOT pointing a specific organ.)
In contrast, 胃 is a word to point specifically "stomach" as an organ, like 胃がいたい。
So I would say おなか is more common :)