After your visit or procedure, your provider sends the bill to Medicare, then your Medigap plan covers out-of-pocket costs that you are responsible for after Medicare has paid their portion of your medical costs. You could have low to zero out-of-pocket costs, depending on what letter Medigap plan you choose.
Once you enroll in Medicare Part B, you will have a six-month window to enroll in Medigap insurance without having to answer health questions and go through medical underwriting. Once this window has passed, you can still enroll in a Medigap plan anytime, but you must pass medical underwriting.
No, they are not the same. You leave Original Medicare when you sign up for Part C, while Medigap/Medicare Supplement plans work with Original Medicare to provide you more comprehensive benefits than Original Medicare has to offer.