In practical terms, when flying the usual types of trainer that you find in most flying schools:-
Use the "Utility Category" limits in the aircraft's POH, for all training flights: including students under training, flight tests, school check flights for qualified pilots.
In particular, most schools insist on the lower "Utility Category" MAW being used for such flights, presumably for safety reasons and because it puts less stress on the airframe.
Use the "Normal Category" limits when planning a self-fly-hire cross-country trip with passengers.
I hope that this helps
