Standard Lease - Legal Document that is typically 12-months, but can be any time period, between one person who owns property (Landlord) and allows someone else to occupy it (Tenant). This is the most widely used form in the world and chances are if you are looking to lease a property, you will be asked to sign one of these.
Month to Month Lease - Legal Document for any period of time between a landlord and tenant. The general rules that apply are that the Landlord must give the Tenant 30-days notice of any rental increase and the Tenant must give the Landlord 30-Days notice of any intention of leaving the property.
Sub-Lease - Legal Document is between a Tenant already renting a particular property for a period of time, and decides to re-rent the property to someone else (Sub-Lessee). Most leases do not allow for the sub-leasing of property, at least in residential. This form is most common amoung college dormitories and multi-room apartments in urban-areas in order to reduce rent.