A Montreal chauffeur service is private ground transport booked in advance at a fixed price and carried out by a licensed chauffeur operator working under Québec's Act respecting remunerated passenger transportation by automobile. The SAAQ authorises each driver and each vehicle, and the Commission des transports du Québec authorises the operator's transportation system. You cannot hail one on Sainte-Catherine Street. The car, the chauffeur and the total are agreed before the ride, whether that is a YUL airport transfer, an hourly car service in Montreal or a black car to a meeting downtown.
What you are buying is predictability. App fares climb when the A20 backs up, a snowstorm closes lanes or a festival lets out, and at YUL the redevelopment has made the kerb itself unreliable at times. A reserved Montreal car service fare does not move with any of that. It already contains the 5 percent GST, the 9.975 percent QST, the C$0.90 government fee Québec charges on every paid trip, and any bridge toll on the route.
The same booking reaches well past the island. MET airport transfers for Porter flights into Saint-Hubert, cruise transfers from the Old Port, YUL to Laval and the South Shore, and a fixed fare up to Mont-Tremblant or along the river to Quebec City. If you are comparing against a cab, the Montreal taxi alternative page sets out the difference, and teams with regular arrivals can run everything through corporate travel in Montreal.