A shelf is a flat, horizontal plane used for items that are displayed or stored in a home, business, store, or elsewhere. It is raised off the floor and often anchored to a wall, supported on its shorter length sides by brackets, or otherwise anchored to cabinetry by brackets, dowels, screws, or nails. It can also be held up by columns or pillars. A shelf is also known as a counter, ledge, mantel, or rack. Tables designed to be placed against a wall, possibly mounted, are known as console tables, and are similar to individual shelves.
A simple wooden wall shelf
A wooden shelf with a great number of different hair colours in a hairdresser shop in Germany
Adjustable shelving made from Dexion steel slotted angle
Two stainless steel shelf supports placed relatively far apart.
A bracket is an architectural element: a structural or decorative member. It can be made of wood, stone, plaster, metal, or other media. It projects from a wall, usually to carry weight and sometimes to "...strengthen an angle". A corbel or console are types of brackets.
A classically detailed bracket at the chapel of Greenwich Hospital, London
Bracket for a shelf or hanging items
Brackets are used in traditional timber framing, including the support of a jettied floor which can be carved. Magdalene Street, Cambridge, England. Sixteenth century