I don’t understand this, isn’t a franchise someone who operates under a brand that they are franchise of?

The operator is the one operating, no need to say it is different for postal services. Brand is fine for the brand while operator refers to the name of a business (or public entity etc.)
We could suggest to omit operator if we suppose it is already implicit with the brand, but it doesn’t make it “wrong” to put an operator tag for the operator, at most it could be seen as redundant.