When you lease a car, the car is yours to drive and operate - as you would if you were to buy a car. The key differences between the two are the ownership and maintenance of the vehicle.
When you buy a car with cash, you own it. (In Singapore though, most drivers buy a car on a hire-purchase bank scheme. In actuality then, the bank owns it until you pay off the loan!) When it comes to car leasing, the car leasing company owns the car you drive.