Great Britain

• playbox

  A box for a child's toys and personal things (especially at a boarding school).

• tuck box

  A box for storing eatables (especially at boarding school).

Chest

• chest

  Box with a lid; used for storage; usually large and sturdy.

• lid

  A movable top or cover (hinged or separate) for closing the opening at the top of a box, chest,...

Also contains

• strongbox

  A strongly made box for holding money or valuables; can be locked.

• casket

  Box in which a corpse is buried or cremated.

• crate

  A rugged box (usually made of wood); used for shipping.

• carton

  A box made of cardboard; opens by flaps on top.

• poor box

  Box for collecting alms, especially one in a church.

• snuffbox

  A small ornamental box for carrying snuff in your pocket.

• ballot box

  A box where voters deposit their ballots.

• paintbox

  A box containing a collection of cubes or tubes of artists' paint.

• base

  A flat bottom on which something is intended to sit; "a tub should sit on its own base".

• cereal box

  A paper box in which breakfast cereals are sold.

• pyxis

  A small box used by ancient Greeks to hold medicines.

• pencil box

  A box for holding pencils.

• matchbox

  A box for holding matches.

• shadow box

  A shallow rectangular box with a transparent front used to protect and display small...

• cigar box

  A box for holding cigars.

• mailbox

  A private box for delivery of mail.

• bandbox

  A light cylindrical box for holding light articles of attire (especially hats).

• hod

  An open box attached to a long pole handle; bricks or mortar are carried on the shoulder.

• casket

  Small and often ornate box for holding jewels or other valuables.

• tinderbox

  A box for holding tinder.

• shoebox

  An oblong rectangular (usually cardboard) box designed to hold a pair of shoes.

• flat

  A shallow box in which seedlings are started.

• window box

  A long narrow box for growing plants on a windowsill.