Almost all of the trains on that route are local trains which stop at all or mostly all stations on the way, with no reserved seats available - like a city bus. They can't sell out. There is no discount available for advance purchase and they are easy to get at the station. Like most Regional trains you just pop on the first train going your way (after getting the ticket of course, and after putting it in the stamping machine) carry your luggage on, and find a seat. Unlike some Regionals throughout Europe, the PACA Regionals are almost all double deckers (sit upstairs if you don't have too heavy luggage, on the left hand side in the direction of travel for the great view of the sea). There are a few trains borrowed from Marseilles used at peak times.
There are also a very few TGV trains between Nice and Cannes each day. They are the very fast high speed trains between Paris and Nice, but they are few, and they must be reserved ahead of time, and the tickets are much more expensive, and if you have a non changeable ticket you need to travel on the exact TGV you have reserved - difficult if you are flying.
They also don't go any faster than the Regionals on that part of the route because of the mountains.
My advice is to get the Regional.
If you take a taxi to Nice Ville, the main station, you will ride the train back towards the airport before passing it and going on towards Cannes.
If you take a taxi to Nice St Augustine, the small station near the airport, the taxi driver will not be happy with such a short trip, and some trains don't stop there, and it is stairs up from the road.
Then again there are no lifts, escalators, or ramps from the tunnel between the tracks up to the correct platform at Nice Ville, although there is an escalator to the tunnel from the station main hall.
EDIT: in the time it took me to wear out my fingertips I see many of my answers have been previously answered...... teamwork!!