Final answer:
Medicare is the federal health care program for those over the age of 65 and the disabled, while Medicaid provides health care for low-income individuals and is administered jointly by the states and federal government.
Step-by-step explanation:
The federal health care program that covers the elderly is known as Medicare. Medicare provides health insurance to those who are over the age of 65, as well as to younger individuals with certain disabilities. On the other hand, the program that offers health care coverage for the poor is called Medicaid. Created in 1965, Medicaid is a joint program between the federal government and individual states, aimed at providing medical insurance to people with low incomes, including families with children, elderly persons, and the disabled. Each state administers its own Medicaid program, setting its own eligibility requirements and determining the level of benefits.