Final answer:
The art that protrudes from the nail but remains part of its background is known as bas-relief, which is a type of relief sculpture with minimal projection.
Step-by-step explanation:
Art that protrudes from the nail is known as bas-relief. Bas-relief is a type of relief sculpture that has minimal projection from its background, unlike sculpture in-the-round which is a freestanding sculpture that can be observed from all angles. Other types of relief sculptures include high relief, where the sculpture projects further from the background, and sunken relief, where the design is carved into the surface.