You would be forgiven for not knowing the difference between the two, or at the very least confusing the two, because they not only sound very similar, but they also have the goal of helping people who are in need of medical care. But there are some profound differences between Medicare and Medicaid that people need to know about so that they can properly apply for, and hopefully use, these programs.
Medicaid is a federal program that helps low-income individuals get medical care. Though it is a federal program, each state runs it separately with different rules in each state. Medicare, on the other hand, is paid into over time by people, and then those people may eventually fulfill their requirement to earn Medicare benefits. This system is federally run and has uniform rules, and it is primarily for older people who are financially constrained but still obviously need medical care.
You can qualify for both, but qualifying for one doesn't guarantee you will qualify for the other. Medicaid and Medicare have separate requirements and processes.
To qualify for Medicare, a person needs to be 62 years of age. You can qualify is you are younger, but a serious Social Security disability situation needs to be present. Medicaid has no age requirement.
The benefits are also different between the plans. Medicaid covers some basic medical care, while Medicare has more comprehensive coverage -- though it depends greatly upon which Medicare plan you are on (Part A, Part B, and Part D).
Source: FindLaw, "The Difference between Medicare and Medicaid," Accessed May 5, 2015