Swallowing is referred to in medical terms as deglutition. Swallowing is actually a reflex which is initiated when a food or beverage is pushed backwards into the back of the mouth (pharynx) by the tongue. The food or beverage is then automatically (involuntarily) pushed down the tube to the stomach (esophagus).
During swallowing the breathing passage (glottis) in the back of the mouth is closed as a part of the reflex. Thus, breathing is temporarily stopped while swallowing.
A belch is the expulsion through the mouth of gas from the stomach or esophagus. This is accomplished by relaxing the esophageal sphincters (upper and/or lower) and increasing abdominal pressure. The glottis (opening to the trachea and lungs) is closed.