No. Medicare and Medicaid are designed to meet very different needs within the community. In some cases, an applicant may qualify for both types of plan, but it is more common for them to fit into a single type of coverage, or to not qualify for government assistance at all.
Medicare is meant specifically for people who are either over the age of 65 or fall under a specific list of disabilities or diseases. For instance, medicare would cover you if you developed kidney disease and had to have daily dialysis or a transplant. It would not cover you if you were a young mother without any other type of health insurance unless you were able to qualify under the disabilities portion of the program.
Medicaid is meant for people who suffer from a wider list of disabilities or have a very low income. Young single mothers generally qualify for Medicaid, and it may be available for your children and babies even if it is not available to you. The purpose of Medicaid is to make sure that at risk families are able to get the minimum care they require, including child medical care, and health care for the ill and indigent.
Typically, Medicare is described as government health care for the elderly or terminally ill, and Medicaid is thought as government sponsored health care for the poor and destitute. Both are designed to reach a specific high risk portion of the population, but they are designed for different ends of the health care spectrum.