//The difference is obvious to me.//
Well it's not to me. Face coverings, we are told, are to prevent possibly infected people spreading the virus. So, if a home made mask is good enough to wear in a restaurant or pub (when not eating/drinking, obviously), it's good enough in a supermarket or on a train or bus, why isn't one good enough when sitting waiting for a blood test in a hospital? Conversely, if a more robust mask is needed to protect people when mooching about in a hospital, why isn't one necessary when on a bus, in the freezer aisle in Tesco's or waiting your turn in the barber's?
If people need protecting, they need protecting. If a lump of damp rag is good enough in Tesco's it should be good enough in a hospital.