Medicare is a federal health insurance program. It serves people 65 and older, younger disabled patients, and dialysis patients. Patients pay part of costs through deductibles. Small monthly premiums are required for non-hospital coverage. Medicare is also a federal program run by a federal agency (the Centers for Medicare & Medicaid Services), so it is essentially the same everywhere in the country.
Medicaid is an assistance program. It serves low-income people regardless of age, and patients usually pay nothing, or a small co-payment, for covered medical expenses. It is a federal-state program, which means it is run by state and local governments within federal guidelines. Consequently, who Medicaid covers and how it works varies from state to state. There were about 82.9 million Medicaid beneficiaries as of 2018.