There are no published differences in phraseology for 'basic' GNSS approaches and Baro/VNAV approaches in the UK that I'm aware of.
'Request R-NAV approach' and 'Cleared R-NAV approach' is pretty much it. You can add runway designators or via waypoints to that too.
I guess it may become necessary when airfields have more than one RNAV approach to a runway to define them in some way via another designator or phrase. How many airfields have Baro/VNAV approaches now? I'm a bit out of the loop but I thought Alderney was due to be the first a couple of years ago?