I hung my clothes on the hanger which I hung on my clothes rack. I hung my jacket on the coat stand. You hang your clothes on a hanger and usually hang the hanger on the clothing rack. A coat stand is usually free standing that you put all jackets on. Hope that helps!

A clothing rack is the horizontal pole in your closet that you hang your clothes on (but I think it's more common to call this a "clothing rod"). A clothing rack can also be a pole or a circular stand like the ones you find in department stores. i.e., "She found a cute dress on the clearance rack at Macy's." A hanger is the hooked, triangular thing you put inside a shirt (or whatever) before you hang it on a clothing rod. i.e., "I prefer plastic hangers over wire hangers. Wire hangers get bent too easily." A coat rack is the tall, vertical pole that has hooks on it for your guests' coats, scarves, etc. They're the things people usually keep near their front doors. i.e., "There's a coat rack near the door, if you don't want to wear your jacket inside." They're not interchangeable, but they are similar concepts.