The difference between "peat moss" and "sphagnum moss" when we're talking about garden supplies is tricky. Sphagnum moss is the live moss that grows in peat bogs. It's harvested while still alive. People use sphagnum moss to decorate potted plants or to line wire baskets for planting. Sphagnum moss that was harvested while alive isn't a soil amendment like peat moss.  Peat moss is sphagnum moss that's been dead and decomposing underwater for centuries. Through that decomposition process, it becomes useful for your soil.