If you have Original Medicare and you buy a Medigap policy; Medicare will pay its share of the Medicare-approved amount for covered health care costs. Then, your Medigap policy pays its share. Medigap policies have premiums. Medigap policies differ from Medicare Advantage plans. A Medicare Advantage Plan is a way to obtain your Medicare benefits, whereas a Medigap policy supplements your Original Medicare coverage. Medigap policies can’t be sold to anyone enrolled in a Medicare Advantage Plan. If you have Medigap and switch to enroll in a Medicare Advantage Plan for the first time, you have the right to change your mind. You have special rights under federal law to purchase a Medigap policy if you return to Original Medicare after 12 months of enrolling in the Medicare Advantage Plan.