Tear away backing is a lighter weight backing than cut away.
Tear away backing can be torn away from the embroidered garment, where as cut away backing will need to be cut away with scissors.
Tear away backing is suitable for standard materials and garments, such as t-shirts, polos, hoodies and other gaments that do not require as much stability.
Cut away backing is suitable for lightweight garments, such as sports wear, silk, lycra and other garments that require more stability.