What is the name of the pus-containing abscess that involves the entire hair follicle and adjacent subcutaneous tissue?

The correct term for a pus-containing abscess that involves the entire hair follicle and the adjacent subcutaneous tissue is furuncle. A furuncle, commonly known as a boil, develops when bacteria infect a hair follicle, leading to inflammation and accumulation of pus. It typically manifests as a painful, red lump that may drain pus when it ruptures.

This condition can occur anywhere on the body but is particularly common in areas where hair follicles are present and are subject to friction or irritation. Unlike a comedo, which refers to a clogged hair follicle without infection (like a blackhead or whitehead), or a pustule, which is a small elevation of the skin containing pus but does not involve the entire hair follicle, a furuncle specifically indicates infection and inflammation affecting the hair follicle and surrounding tissue.

Similarly, a carbuncle is a more severe form that consists of a cluster of furuncles that may connect to each other, leading to a larger area of inflammation and pus formation. Thus, the characteristics of a furuncle align perfectly with the description given in the question, making it the correct answer.