Final answer:
The red, moist area with fluid-filled vesicles should be documented as a second-degree burn by the nurse, typically requiring a clean and sterile environment to heal properly.
Step-by-step explanation:
The nurse should document that the client with a burn on the arm that is red, moist, and covered in shiny, fluid-filled vesicles is suffering from a second-degree burn. This type of burn, also known as a partial-thickness burn, affects both the epidermis and a portion of the dermis layer of the skin. It is characterized by swelling and blistering. The goals for treating a second-degree burn include keeping the burn site clean and preventing infection. These burns typically heal within several weeks with proper care. Maintaining a sterile environment and close monitoring for signs of infection are key aspects of management for these burns.