Simply a Medigap or Medicare Supplement pays dollars for you for covered services. Medicare determines what is covered not the plan. All supplements of the same letter provide the same medical benefit. The only difference is price.
Medicare Advantage plans are private insurance policies similar to what people have prior to becoming Medicare eligible. Most if not all of the monthly premium for these plans is paid by Medicare. Once a person enrolls in an advantage plan they no longer receive benefits from Medicare. All care is via the insurance company.
Which one is right for you is a discussion you should have with an independent insurance agent. We have over 25 years of experience working with Medicare beneficiaries for both Medigap and Medicare Advantage Plans. Make sure your agent can help you with all options.