Medicare is a federally funded system of health care incorporated into the Social Security Act of 1965. It's purpose was to provide health care for persons over age 65 who were/are legal residents of the U.S. for at least fifteen years. It is available to persons with congenital or permanent disabilities regardless of age. It pays 80% of all qualifying medical expenses, the remaining 20% must be paid by private insurance or by the covered individual himself. It is funded by a payroll tax of 2.9% of which half is paid by the employee and half by the employer, unless one is self employed in which instance one must pay the entire 2.9%. If one has paid the tax for not less than 40 quarters (10 years) there are no additional premiums payable; however, if one qualifies for Medicare and has not paid the tax for 40 quarters, a premium will be assessed. There are additional provisions/qualifiers discussed in more detail at the links noted below.
Medicaid is a federal program to provide medical insurance for persons with limited income. Eligibility is determined by ones means to pay, rather than ones age, as in Medicare. Any person over 65 who meets the requirements set forth above qualifies for Medicare; but the requirements for Medicaid are more narrowly defined. Medicaid is only partially funded by the federal government; it is also funded by the individual states who manage the program and the administration of its benefits. All fifty states participate in the Medicaid program.
Medicare is a federal system of health insurance for people aged 65 years and older and certain people at younger age with a disability as for Medicade, it's just a health insurance for those who are requiring financial assistance.