Biblio's answer seems to me precisely to represent BrE usage as well...A "piggy bank" is either an item in which a child will store his savings, usually with a slot for coins or bills and normally has a fanciful or funny shape. Figuratively, it could be used in an informal manner to refer to a person's savings.
"Money box" would, in my experience, be used almost entirely in a literal manner: a box in which money is stored.
Is there any context? Are you interested in an AE or BE take on the question?
I agree, and would add that piggy banks are designed to keep money relatively inaccessible, and cash boxes, as MJRupeJM explains, are added to and taken from in the course of transactions.I think in AE, money box is synonymous with cash box.
I imagine a cash box as a rectangular metal box with a tray inside to sort cash bills, used where a cash register is not available (at flea markets, roadside stands, ticket booths, school plays, etc.)
I would think a "container in the shape of a pig" would almost always be called a "piggy bank."Hi!
I mean, can I define a container in the shape of a pig *money box*?
But not to me! I take "money box" to mean any receptacle with a slot into which coins are deposited - of which a piggy bank is one example. A cash box being a (usually rectangular) box with a hinged lid and lockable with a key.Biblio's answer seems to me precisely to represent BrE usage as well...