Your understanding is correct. In an assignment, someone else takes over the lease for  you; they step into your shoes and become the tenant in your place. In subleasing, you become the landlord renting to them. Assignment exposes you to less liability; once assigned, you're out of the picture. However, many leases and other contracts restrict the right of one or both parties to assign the lease or contract, and such a restriction is enforceable. So your son should check his lease to see what he is allowed to do, though if he can assign the lease, then he is probably better off doing that (unless there's some reason he'd like to reserve possession or control over the apartment).