Stanch is merely an alternative spelling of staunch. The preferred spelling is staunch.
Staunch has two very different meanings.
As a verb, staunch means “to stop the flow of (liquid)”—using pressure, or by blocking the flow; you cannot use staunch for turning off a water faucet. “To staunch the flow of blood from a wound” is the most common usage. However, it can be used metaphorically, for anything that “flows,” such as tears or money.
As an adjective, staunch describes strong resistance or opposition. It implies strength or passion and usually describes people or their actions:
My brother Tim is a staunch opponent of the death penalty.
This means that he is very strongly opposed to the death penalty.