Well according to the Census Bureau this is the official definition of Medicare and Medicaid.
Medicaid
Medicaid is a program administered at the state level, which provides medical assistance to the needy. Families with dependent children, the aged, blind, and disabled who are in financial need are eligible for Medicaid. It may be known by different names in different states.
Medicare
Medicare is the Federal program which helps pay health care costs for people 65 and older and for certain people under 65 with long-term disabilities.
The Census Bureau has a total of thirteen definitions for various types of health care insurance.
