A 403(b) retirement account is sponsored by a non-profit employer – such as a hospital, university, or municipality. They work much the same way as their for-profit counterparts, the 401(k).
The 457 plan is generally available to employees of governmental and municipal entities. They work much like IRAs, but there is no 10% penalty for withdrawals before age 59 1/2.
This is a synopsis of the Medicare program – Parts A, B, and D.