The stomach is an organ used to digest food, it is just one part of the digestive system.
In 2152, Porthos came down with a little gastrointestinal distress, because Captain Archer had fed him cheese again. Doctor Phlox gave the Captain the advice not to feed any more dairy products to Porthos. (ENT: "Dear Doctor")
Due to the brak'lul, Klingons have, among other things, a redundant stomach. Tom Paris believed that this meant that Klingons were incapable of getting nauseated and was surprised when B'Elanna Torres stated how ill she felt. This was also proven false when Worf experienced space sickness in zero G environment.(TNG: "Ethics"; VOY: "Macrocosm"; Star Trek: First Contact)
The Vok'sha from planet Rakella Prime believe that 'hate' is a beast that lives inside the stomach. Their greatest mythical hero is a man who ate stones for 23 days to kill the beast, and became a Saint. (VOY: "Heroes and Demons")