Medicare Part C is known as Medicare Advantage. These are private plans run through Medicare that, by law, must at least be "equivalent" to regular Part A and Part B coverage. But there's lots of variation among Part C plans. Any given one may cover less of one thing and more of another than Parts A and B do. (Confusing, right?)
Some Part C plans provide significant coverage beyond what you get in Parts A and B - including, in some cases, prescription drug coverage - but not all. The better ones basically function like Medigap policies but are administered by Medicare rather than being wholly run by private insurance companies.
In fact, if you have a Medicare Advantage plan, any Medigap policy you may have is useless; Medigap won't pay if you are covered by Medicare Part C.
The monthly premium varies widely depending on your state and the private insurer you choose, as well as whether you choose an HMO or PPO for your Medicare Advantage coverage.
To compare Medicare Advantage plans, go to the Medicare Web site [please link to: (Note: Medicare Advantage Plans are labeled "Medicare Health Plans" at the Web site.)