What is the difference between the Medicare and Medicaid programs? Medicare provides health care for older people, while Medicaid provides health care for people with low incomes. Medicare provides food stamps for people with low incomes, while Medicaid provides housing for people with low incomes. Medicare provides food stamps for older people, while Medicaid provides housing for older people. Medicare provides housing for people with low incomes, while Medicaid provides health care for people with low incomes.