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")
When Lwaxana Troi was attracted to Odo in 2369, he attempted to lose her interest in that he couldn't eat as he did not have a stomach. (DS9: "The Forsaken")
Lurians have two stomachs. They can use their second stomach to store liquids for several years. (DS9: "Who Mourns for Morn?")
Due to the brak'lul, Klingons have, among other things, a redundant stomach. (TNG: "Ethics"; VOY: "Macrocosm")
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")
Ferengi Rule of Acquisition No. 214 states "Never begin a negotiation on an empty stomach.". (DS9: "The Maquis, Part I")