Final answer:
TRICARE is the program that provides health insurance coverage to active-duty service members, retirees, and their families, while the Veterans Health Administration offers services to military veterans.
Step-by-step explanation:
The government-sponsored program that provides coverage for active-duty service members of the armed forces (ADSM) is the TRICARE program. TRICARE is a healthcare program serving Uniformed Service members, retirees, and their families worldwide. It effectively acts as a form of health insurance, offering a wide range of plans and benefits, much like civilian health insurance, to ensure that members of the military and their dependents have access to medical services.
Military veterans also have access to specific healthcare programs, among them the Veterans Health Administration, which oversees services provided to U.S. veterans, including healthcare services and benefits programs. Another key program is Medicare, which offers healthcare to people over the age of 65 and those who meet disability standards, while Medicaid serves individuals and families with low incomes who meet other eligibility requirements.