A Tillandsia is a Bromeliad...but not all Bromeliads are Tillandsias. Bromeliad is the Family name. Tillandsia is the genus.
Airplants are the common name for Tillandsias (sometimes called "Air Plants"). Not all Bromeliads are Airplants. Airplants grow without soil while most types of Bromeliads do best in soil.