I've heard "chester drawers," once in a great while. It does sound odd to me; I'd wonder, "Who is Chester?" In fact, I didn't hear "chest of drawers" much until I moved to the deep south. It seemed like a lot of words to describe an item, TBH. We said "dresser."
Chest of drawers is the UK term for it. Over here, you'll find a dresser in the kitchen - a free standing (usually) piece of furniture made of cupboards with shelves above it - something you might possibly call a hutch? Over here, a hutch is an outdoor 'crate' type home for a pet rabbit...
Divided by a common language, indeed.
Yeah, a dresser is for things you'd dress yourself in. A hutch is either the thing in the dining room (which might also be a buffet or a sideboard or a cabinet) OR the rabbit thing (which I don't know an alternative U.S. name for except a cage, I guess).
Also, I think you guys use "cupboard" a lot more than we do, though it means more or less the same thing here -- we just use "cabinet" more frequently. Also I think you use cupboard for things we'd call closets (part of a room) or wardrobes (freestanding, tall clothes containers).
Weird stuff I've seen on CL lately -- lots of homemade or extraordinarily ugly cat towers. And a 'barely used' cat toilet training kit, which I guess maybe isn't quite as gross as barely used human toilet products, but still strikes me as icky, irrationally. (Yeah, we got a cat.)