What do they mean?
Subletting is when the original renter cannot fulfill their lease and finds another to rent the property. The landlord is fully aware of this transaction as the new renter signs an agreement with them. A subletting arrangement allows the current renter to leave without any penalties because someone else is replacing them. The replacement can be suggested by the renter but must be approved by the landlord.
Subletting is a great choice when the current renter needs to break their rental agreement for any particular reason. Whether he has a family emergency or has to relocate for work, they can find a suitable tenant that the landlord approves to take over the rent and sign a new rental agreement.
Subleasing is when the renter whose name is on the rental agreement rents a room or the property to another renter under the table. Landlords normally have no knowledge when this happens because it can be illegal.
Most landlords/property managers do not allow subleasing for many valid reasons. For one, this creates a problem if something is damaged in a home. Let's say the person leasing the home (the sublessee) breaks something which the person who rented to them (the subleaser) is fined for. This can create problems for everyone involved.