Is a Post Office(TM) a real post office or a mailing service?

The USPS website lists locations that are Post Office™ sites. Doesn’t the™ mean that these are all commercial services that will handle postal mail and packages, UPS parcels, etc., and don’t they charge extra for it? The USPS website does not make it easy to find real United States post offices. I want to pay for the postage only and not some commercial rate, but I need to understand what I’m looking at when I see the listings.

Or am I wrong and these all do charge only standard USPS rates for packages without any surcharge?