There are 3 basic types of breathing types for singers:
Shoulder breathing (breathing from the shoulders which is highly unreccommanded, considering you can only reach 30-40% of your breathing compasity.
Stomach Breathing (breathing from the stomach is what most choir teachers instruct because its an easier exercise that reaches to 70-80% breathing compasity.
And last is the Diaphram breathing(breathing from the hips to the top of the rib cage. Here, you can reach the full 100% of breathing compasity. MOST choir teachers only mention this in passing because it's EXTREMELY hard for even the most experienced singer to always reach this stage.