Final answer:
The Medicare program is managed by the Centers for Medicare & Medicaid Services and offers contracts to private health care companies for certain plans, while states administer Medicaid with federal guidance and also contract with private companies for managed care plans.
Step-by-step explanation:
The Medicare program is administered by the Centers for Medicare & Medicaid Services (CMS), a federal agency within the United States Department of Health and Human Services (HHS). CMS contracts with private health care companies to provide Medicare Advantage Plans (Part C) and prescription drug plans (Part D), expanding choices beyond the original Medicare (Part A and Part B) benefits. The Medicaid program, on the other hand, is a joint federal and state program that provides health care to those with low incomes, including families with children, the elderly, and the disabled. Medicaid is administered by states within federal guidelines, and states contract with private health care companies to manage Medicaid benefits through managed care plans.