Parts of a Bed, Headboard and Mattress (Diagrams)

Parts of a Bed, Headboard and Bed Frame (List):

Headboard slat: Vertical grid or screen attached to the back of the bed frame.
Headboard top rail: The horizontal piece set on top of the headboard slat.
Headboard cross rail: The horizontal piece set below the headboard slat that supports the bed base.
Bed side rail: Also known as cot sides, safety sides and bed guards, these are those parts of the bed that run from the headboard to the footboard and support the bed lengthwise.
Bottom side rail: Wood or metal pieces that run below the headboard to the footboard.
Footboard slat: Decorative piece of vertical panel attached to the front of the bed frame.
Headboard leg: Vertical parts at the opposite sides of the headboard slat used so that the headboard sits at the desired height.
Cleat: The area that serves as base for the bed to which cut slats are attached.
Footboard top rail: Vertical grid or screen attached to the front of the bed frame.
Cut slats: Thin narrow pieces cut in desired lengths and widths that create a series of overlapping grid or screen at the base of the bed.

 Awesome diagram illustrating the different parts of a bed, bed frame and mattress (cross section cut so you can see the interior parts of a mattress). 

More: 43 Types of Beds & Types of headboards

Parts and Layers of a Mattress

HD PU foam (High Density Polyurethane Foam): Plastic with an open cellular structure that makes it flexible or rigid and used for comfort by providing support to mattresses, upholstered furniture and car seats.
Double foam quilt: A two-sided quilted mattress.
Memory foam: Made of polyurethane and other chemicals, it’s designed to mold to the body in reaction to body heat and pressure and has the beneficial effects of providing relief from back/spine pain and pressure points, among others.
Polyester padding: A mattress’ non-woven, thermally bonded component designed to feel either soft or firm and to provide comfort.
Springs: Resilient metal coils used to support the bed mattress.
Cotton felt: The mattress component that separates the coil system from the cushioned layers of the bed.
Quilt: A warm decorative bed covering usually made of three layers of padding stitched together.