Lease - Company drivers can choose to hire their cars for a set period, paying a monthly fee. Contract hire is known as an 'operating lease' while leasing is technically a 'finance lease'.
The main difference is that under contract hire, the responsibility for the car remains with the leasing company, whereas with a lease it is with the driver.
Another difference is that at the end of the term, contract hire cars always return to the leasing company, but under a straight lease, the driver may be able to buy the car. (See Contract hire.)