There is no difference; they mean the same thing, they are just different names for the same concept. Supplement plans/medigap plans are built to help fill in the gaps that Medicare doesn’t cover. They are extra coverage plans that you can buy from private insurance companies that help pay your share. Whatever is left from what Medicare covers under the approved Medicare amount is then passed on to your Medigap/Supplement policy for it to pay its share. 

They are different from Medicare Advantage in the following ways: Medicare Advantage is another way to get your Medicare Coverage besides the true original Medicare, while the supplement plans only help pay for the cost/share that Original Medicare doesn’t cover. The following are not typically covered by Medigap plans: long-term care, vision, dental, hearing aids, eyeglasses, and private duty nursing. You can not purchase a Medigap plan while on a Medicare Advantage Plan.