Trapeze is a bar hanging between two ropes. The bar is a hollow or solid steel tube, or made of carbon fiber. The ropes can either be hung separately (static trapeze) or together (single point or dance trapeze).
Hoop is a metal apparatus made from a solid or hollow steel tube. The tube is about 1″ in diameter, the hoop itself is anywhere from 30-40″ in diameter. It is often covered with cloth tape.
Aerial silks is a long piece of fabric that is rigged from the ceiling by the center of the fabric, so the two ends of the fabric hang down. Though it’s called silks, the fabric is actually made of nylon.