THe way this game works is it's just an open world, all the time. There are other cars in it - most are computer controlled, but up to six are players. They can do whatever they want - race against each other, against the AI, etc - racing against someone else is as simple as just driving by and when you see them you issue a challenge by pressing L1. THey accept, and the race is on.
So - when you pllay with just two of you, the rest of the world is populated with AI - but to the games credit it is often difficult to tell them apart.