A lease agreement generall specifiys a period of time that you are obligated to make payments. Even if you no longer want the item you still have to pay the entire period. A rental is typically month to month or payment to payment. If you want out, simply return the item and stop paying.
Contracts however can be written any way you want. So a lease agreement could be month to month and a rental could be for a fixed period or number of payments. It all depends on how the agreement is written.