A lease is a contractual arrangement calling for the lessee (user) to pay the lessor (owner) for use of an asset.
The narrower term rental agreement can be used to describe a lease in which the asset is tangible property. Language used is that the user rents the land or goods let or rented out by the owner. The verb to lease is less precise as it can refer to either of these actions. Examples of a lease for intangible property are use of a computer program (similar to a license, but with different provisions), or use of a radio frequency (such as a contract with a cell-phone provider).
The term rental agreement is also sometimes used to describe a periodic lease agreement (most often a month-to-month lease) internationally and in some regions of the United States.