Mayo Clinic Jacksonville puts out an official letter to it's patients regarding open season for Medicare enrollment. I think it helps explain the differences and why so important to know exactly that Medicare Original/Traditional is Federal Medicare and when you go to Medicare Advantage you are moving to a private company coverage not federal Medicare.
Below is official letter put out by Mayo Clinic Jacksonville yearly on this insurance subject.
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At Mayo Clinic, our patients are at the center of everything we do, and your trust is very important to us. Sharing information is one way to help ensure we continue to be trusted partners for your health care needs.

As you may be aware, beginning in mid-October, it will be time to select health care coverage for 2024. Mayo Clinic in Florida is not in-network with most Medicare Advantage Plans. We want to be sure that you are aware that Mayo Clinic in Florida will not schedule appointments for patients with out-of-network Medicare Advantage Plans.

Many patients are making elections for their coverage in 2024, including Medicare. Marketing for Medicare Advantage Plans may indicate that you can be seen at any facility that accepts Medicare, however Mayo Clinic in Florida is out of network on these plans.

Medicare Advantage Plans are managed by commercial insurance companies on behalf of Medicare and offer a specific network of contracted medical providers and hospitals, which may not include Mayo Clinic in Florida. These plans are required to have a substantial network of qualified providers to accommodate their members' medical needs.

As you consider your options for health coverage, you can confirm Mayo Clinic's participation by providing the insurance plan under consideration the Tax ID information below:
Mayo Clinic Florida Hospital 59-0714831
Mayo Clinic Florida Outpatient Clinic Services 59-3337028

We do accept Original Medicare (Parts A and B), and supplement plans, sometimes referred to as Traditional Medicare. If you choose to enroll in a Medicare Advantage Plan, we can provide your medical records to the next in-network facility you select for your care.

Learn more about your Medicare options online, or by calling Medicare (1-800-MEDICARE), or a State Health Insurance Assistance Program (locate a local resource by calling 877-839-2675). Mayo Clinic is not authorized to assist with Medicare enrollment decisions.

Please continue to update Mayo Clinic on any changes to your health care coverage.

Sincerely,

Mayo Clinic in Florida Leadership