Question

The two federal government plans that provide pensions for retired workers and health care insurance for the elderly are

Answer 1

Number one is Old-Age, Survivors, and Disability Insurance (OASDI) program, which is commonly known as the Social Security, while the second is the Medicaid program. Pensions are dealt with by the Social Security program while the Medicaid gives the elderly health care.

Answer 2

Health care insurance for the elderly provided by the federal government is called Medicare.  
Social Security is the federal program that provides pensions and other benefits (disability, survivors', etc.).