Find Law gives the following explanation regarding the difference between a rental agreement and a lease:
There is no strict legal difference between a rental agreement and a lease agreement, however in some instances a rental agreement, or a periodic tenancy, may refer to a short-term rental contract. The term can be for any amount of time, but month-to-month tenancies are the most common. Each month the tenancy automatically renews for a new term, unless the landlord or the renter ends the tenancy by giving a 30 day written notice. Changes to the terms of the rental agreement can be made by giving the appropriate written notice.