"erosion" is typically associated with larger expanses of beach, such as, say, "Daytona Beach saw a lot of erosion", etc. "Cuts" are usually referred to on a much smaller scale, for instance, you can still find cuts in areas that have experienced a lot of erosion. Cuts can show up anywhere and for a number of reasons, waves, cross currents, etc., anything that can serve to carve or dig away the sand in any manner that leaves a type of noticeable cut, or deep scar, if you will.