There is no difference between a residential contract and a residential agreement. They are all one in the same. Typically in the sales world these different terminologies were created.
Salespeople realized the negative connotation of the term residential contract and began using residential agreement instead. A residential lease is simply more explanatory in what type of residential instrument you are signing.
There is the rare exception when an agreement has been reached between the tenant and the landlord for another action during the lease term, like tenant performing some contracting work where a residential agreement is needed in addition to the residential lease agreement. A company like RDS Real Estate can help you to determine the meaning of residential leasing instruments.