Medicare is an insurance program. Medical bills are paid from trust funds which those covered have paid into. It serves people over 65 primarily, whatever their income; and serves younger disabled people and dialysis patients. Patients pay part of costs through deductibles for hospital and other costs. Small monthly premiums are required for non-hospital coverage. Medicare is a federal program. It is basically the same everywhere in the United States and is run by the Centers for Medicare & Medicaid Services, an agency of the federal government.
Medicaid is an assistance program. It serves low-income people of every age. Patients usually pay no part of costs for covered medical expenses. A small co-payment is sometimes required. Medicaid is a federal-state program. It varies from state to state. It is run by state and local governments within federal guidelines.