An assignment transfers the lessee’s entire interest in a lease to another party, making them directly responsible to the landlord. A sublease involves transferring only part of the lessee’s interest while the original lessee retains some rights or interests under the original lease.
For example: Bob leases his shop to Trisha for two years (assignment), so Trisha now deals directly with Bob’s landlord. If instead Bob lets Trisha use his shop for six months while he’s away (sublease), Bob remains responsible to his landlord.