Looking at the Welsh rules for face coverings:
The first part seems to be advising some sort of official proof of exemption. The second one seems to be suggesting otherwise.
We advise people to carry information if possible which demonstrates why they have a reasonable excuse (for example a prescription or evidence such as a hospital appointment letter relating to a medical condition). A number of organisations such as transport operators have created cards that can be downloaded from their websites and printed.
The first part seems to be advising some sort of official proof of exemption. The second one seems to be suggesting otherwise.