Hello. The mattress and box spring are just on a normal queen size wood bed frame. We hade it custom made with custom square feet, but you could find something similar from westelm.com. The bed frame just gets pushed into the corner headboard.

Would you say that each headboard is equivalent to a queen (top of the bed) and a king (side of the bed)?

You could probably do that. The bed in the photo is queen. The headboard stops short of the left side by approx 6 inches and stops short of the end of the bed by approx 10 inches. We didn't want it to line up exactly with the edges of the bed. But if you just wanted to buy a queen and a king size headboard and make those into your corner headboard that would work. That's probably an easier way to make it, than trying to make them at a custom size. Good idea.