The random stopping is definitely possible. I think we all know that if an officer indicates to us that we are to stop and pull to the side of the road, then we are obliged to do so, and that's under provincial law.
As I said, once you roll down the window, he'll start asking you some questions about whether you've had a drink, and he'll ask you to show your driver's licence and your registration. That police officer is looking for clues, such as the smell of alcohol, your fumbling with your documents, or something to develop the suspicion of alcohol. Only then can he ask you to provide a breath sample into an approved screening device. Under what's called random breath testing, the police officer, for whatever reason he may have pulled you over, purely randomly, can say, “Show me your registration and your licence, and, by the way, prove your sobriety by blowing into this approved screening device”. That's the fundamental difference.