Final answer:
A bacterial infection with pus at the nail matrix, known as a purulent infection, is typically referred to as paronychia. It can be caused by various bacteria, commonly including Staphylococcus aureus, and can lead to serious complications if not treated promptly.
Step-by-step explanation:
A bacterial infection with pus at the nail matrix is known as a purulent infection or specifically a paronychia when located around the nail. Such infections can be caused by a wide range of bacteria, including Staphylococcus and Streptococcus species. The nail matrix itself is a deep layer of epidermal tissue at the proximal end of a nail where nail growth occurs; when infected, it can produce symptoms such as swelling, redness, and the accumulation of pus. Bacterial cultures and additional testing, such as Gram staining, can reveal that the infection may be caused by spherical, gram-positive bacteria forming grape-like clusters, characteristic of Staphylococcus aureus. This pathogen is a common cause of wound infections and, if left untreated, can become more serious, leading to further health complications.