Rent is a payment to a landlord for occupying a property. Mortgage is a repayment of a bank or credit union loan for buying a house. Lease is a long-term arrangement that works the same way as rent. Rent is a short-term agreement between the landlord and the tenant. When the tenant leaves the property, he is not obligated to buy it from the landlord. In a lease, however, the contract is unchangeable once signed. When a lease period is over, the lessee is typically asked to buy the property.