Medicare Part C is also known as Medicare Advantage. These are private plans that are run through Medicare. Medicare requires that they be “equivalent” to Part A and Part B coverage. That equivalency does not mean they are identical in coverage to Part A and Part B. A Medicare Advantage plan may cover less of one thing but more of something else than what is covered under either Part A or B.
Some Medicare Advantage plans will provide you with significantly more coverage than anything provided by Part A and B, often including prescription drug coverage. In that way, they are similar to a Medicare Supplemental or Medigap plan. The difference between them though is that they are administered by Medicare rather than private insurance companies.