Diaphragm breathing works slightly differently and has certain distinct features. When upper abdomen is pushed out, diaphragm is sucked down to force the lungs in the cavity to expand and inhale. Chest breathing requires the muscles around the lungs to initiate inhalation that fills the lungs forcing the diaphragm extend downwards. (Just expanding chest won’t necessarily force inhalation.)
Hence, diaphragm breathing compels fuller inhalation and deep breathing.
Diaphragm breathing also helps massage Manipura chakra which is a storehouse of debris from negative and stressful emotions. Sedentary lifestyle, fatty food, lack of exercise makes muscles around the daphragm tight and inelastic. Efforts to do diaphragm breathing exercises these muscles.