There is at least a third type of bed. One with the "platform" entirely separate and self supporting. (like you show, but with head and foot boards.
The head and foot board are joined and held upright by a railing that does not support the mattress. Or the head and foot board are supported by the ends of the platform. The bed that I now sleep in is of this latter type with the headboard hung off the head of the mattress frame.
A forum community dedicated to professional woodworkers and enthusiasts. Come join the discussion about shop safety, wood, carpentry, lumber, finishing, tools, machinery, woodworking related topics, styles, scales, reviews, accessories, classifieds, and more!