Sublet and sublease are two different words for the same concept. The suffixes of each word, "let" and "lease," both mean to rent out a property.Subleasing, or subletting, is when a tenant rents their unit to a new occupant. Also known as a subletting, this arrangement allows someone to rent a home from someone else who is already renting the property. Sublet and sublease are generally two different words that mean exactly the same thing. For example, the words lease and let both mean renting out a property. Chicago law requires landlords to allow tenants to sublease their apartments if requested. Here's what else you need to know about subleasing in Chicago. Unlike Illinois state law, Chicago city law specifically grants tenants the right to sublease a rental unit. Subletting is similar to subleasing in that it involves a tenant renting out a property to another person.