Breathing muscles
The two most important breathing muscles are the intercoastal muscles (the spare ribs) and the diaphragm.
All other muscles are only for support. Often people compensate with shoulders and neck muscles causing cramps, head-dache, tightness etc.
A good belly breath is a result of recruiting the diaphragm in the inhalation. This will result in a slight movement of the belly, massaging the intestines too.