The esophagus, which connects the stomach with the mouth, is not an open tube, but is closed. Similarly, when one belches, a little bubble of air moves up the esophagus and exits at the mouth. I am not trying to argue that belches don't smell. They can and do. The rest of the time, the esophagus closes off the stomach.
Some people think that the tongue and stomach are connected, perhaps through reflux of liquid.
Although I cannot completely rule that possibility out, the smell of tongues has little in common with stomach odors. Furthermore, bad breath can usually be controlled by treatments limited to the mouth itself . From my experience, when bad breath strikes, the stomach is the last place to look for an answer. Similarly, Rashi recommended that one walk a little following the meal, in order to prevent bad breath. Perhaps the ancient religious lore is responsible for the common misconception that bad breath is primarily a stomach thing.