Medicare is an insurance program. Medical bills are paid from trust funds which those covered have paid into. It serves people over 65 primarily, whatever their income; and serves younger disabled people and dialysis patients. Patients pay part of costs through deductibles for hospital and other costs. Small monthly premiums are required for non-hospital coverage. Medicare is a federal program.
Product branding, on the other hand, is a marketing strategy wherein a business promotes and markets an individual product without the company name being front and center in the advertising campaigns or even on the product labeling.
A brand is a product, service, or concept that is publicly distinguished from other products, services, or concepts so that it can be easily communicated and usually marketed. A brand name is the name of the distinctive product, service, or concept. Branding is the process of creating and disseminating the brand name. Branding can be applied to the entire corporate identity as well as to individual product and service names.