A lodger rents a single room - say, a bedroom - in an owner occupied dwelling and generally shares the bath and kitchen facilities, and may have "house privileges". The owner retains full control of the premises and while s/he should be respectful of the lodger, retains full access rights to the room occupied by the lodger.
A tenant, on the other hand, rents living space (an apartment, 1/2 a duplex, a whole house, etc.) that the owner does not occupy and retains a right of possession for a specified term. The landlord is bound by certain rules regarding when and whether s/he may enter the apartment and how much notice must be given in order to terminate the tenancy.

