Public assistance programs can be defined as programs that are meant to help people who are poor and disadvantaged. Of the programs that you have listed, only the last one, “welfare,” is a public assistance program.
The other programs that you have listed are all available to people who are not poor. Everyone who reaches retirement age (or who becomes disabled) is eligible for Social Security. All senior citizens are eligible for Medicare. Both of these are true regardless of income level. A person who had a great job and has lots of money in the bank can still get unemployment compensation.
Therefore, only welfare, which is available only to poor people, is a public assistance program.
Welfare is the only example of a public assitance program listed above. A public assistance program by definition has to help a disadvangated group or individual. More information on welfare can be found at the link provided.