A rental agreement provides for a tenancy of a short period (often 30 days) that is automatically renewed at the end of the period unless the tenant or landlord ends it by giving written notice. For these month-to-month rentals, the landlord can change the terms of the agreement with proper written notice.
A written lease, on the other hand, gives a renter the right to occupy a rental unit for a set term -- most often for six months or a year but sometimes longer -- as long as the tenant pays the rent and complies with other lease provisions. The landlord cannot raise the rent or change other terms of the tenancy during the lease, unless the tenant agrees.
Unlike a rental agreement, when a lease expires it does not usually automatically renew itself. A tenant who stays on with the landlord's consent after a lease ends becomes a month-to-month tenant, subject to the rental terms that were in the lease.
For everything you need to know about rental agreements and leases, get Every Tenant's Legal Guide, by Marcia Stewart and Janet Portmant (Nolo).