The skin underneath the free edge of the nail is the:

The skin underneath the free edge of the nail is referred to as the hyponychium. This area serves as a protective barrier that helps to prevent pathogens and foreign substances from entering beneath the nail plate. The hyponychium is important in maintaining the health of the nail and the surrounding skin, as it aids in securing the nail to the finger. It is located at the distal edge of the nail, making it crucial for the overall integrity of the nail structure.

The other terms relate to different parts of the nail or nail unit. The perionychium refers to the skin that surrounds the nail, while the nail matrix is the tissue located beneath the base of the nail where new nail cells are produced. The nail bed is the area of skin beneath the nail plate that provides support and nourishment to the nail. Each of these components plays a different role in nail health and function, but the skin specifically under the free edge is distinctly identified as the hyponychium.