A simple example to distinguish between the two is when you sit on a couch it doesn't deform much and is comfortable. But if you stand on the couch, it deforms more (and may get damaged). Although the force applied in both cases is the same (equal to the weight of the person), the area over which the force is distributed is smaller in the second case leading to larger stress. So stress (and not force) is used to determine whether or not a body will yield or break or get damaged.