Final answer:
The AAHA offers voluntary accreditation programs for veterinary hospitals. The AVMA, while significant in the veterinary field, does not provide hospital accreditation but focuses on guidelines and policies for veterinary practice.
Step-by-step explanation:
The organization that offers voluntary accreditation programs for the management of veterinary hospitals is the American Animal Hospital Association (AAHA). This association sets standards for veterinary practices and provides accreditation to hospitals that meet a high level of care and practice standards. The AVMA is another key organization within the veterinary field, which focuses on policies and guidelines, such as the AVMA Guidelines for the Euthanasia of Animals, but does not provide hospital accreditation.