If you are eligible for Medicare, but choose a Medicare Advantage Plan, you have opted for private insurance that is outside of Medicare.
Medicare Advantage plans are offered by private companies, e.g. Humana, United Health, Blue Cross, etc., and often include benefits not provided by regular Medicare, such as vision, dental, etc.
This type of private insurance plan must conform in certain ways to the rules of Medicare--such as limiting charges for certain services--but is administered by the private companies which sell the plans. Patients still have many of the rights and protections provided under original Medicare.