I never refer to the "Tower" or "Air Traffic" in this instance. I use phraseology such as the "personnel who work in the building over there...."
I suspect this reflects more your attitude towards the folk in the control tower, than any need to convey to your student pilots, the service being provided....
It should be remembered that there are some GA aerodromes in the UK where ATC is provided for most times but where FIS is provided outside the hours of ATC, for example at weekends. It's therefore, impossible to make any hard and fast rule concerning telephone ident: the key is the R/T ident used and properly pre-briefing yourself via the AIP, Pooleys, Bottlang, etc., before setting out.
The other point is that as far as starting and taxiing aircraft (including air taxiing helis) are concerned there's no difference in the actual service delivered between ATC and FIS; and even ATC - when flying in Class G airspace outside the ATZ - isn't mandatory = potential student pilot confusion!