The problem is caused almost entirely by the term 'PAT testing'. a) much of it is inspection rather than test, and b) it's not just plug-in portable equipment that needs to be tested (fridges aren't portable for instance, but need inspection/test).
As Pete says above, the correct term is ISITEE, and is governed by the code of practice. All is explained in there (well mostly all - it does leave a few things open).
Some hotels put hairdriers, trouser presses etc. on FCUs, but they are not part of the fixed wiring as such, and they need testing (or inspecting, as appropriate).
The deciding factor is not whether the item has a plug on or not.
I wish the term 'PAT test' had never been invented - I spend much time explaining things to people because of this!