These two programs have problems that are very similar, but the solutions to those problems are not necessarily the same.
In both cases, these programs are likely to run out of money in the coming decades. In both programs, people pay into a pool while they are working. When they retire, they start to get benefits. The benefits typically greatly exceed what they put into the pool. With the US labor force aging, it will be harder for workers in coming decades to support the people who are retiring.
The solutions for these programs’ problems are not identical. In my view, the government needs to make Social Security solvent by doing a number of things. It needs to raise the retirement age so that people do not get benefits for as long as they now do. It needs to tax more wages rather than letting all wages above a certain level be untaxed. It should also introduce some degree of means testing by reducing benefits to people with higher incomes. By contrast, the main thing that needs to happen to Medicare is lower costs. Health care costs simply must be contained if Medicare is to survive. This is going to be very hard to do, however, because it cannot be done through very simple actions.