Clutch, e.g (5)
(Other definitions for bag that I've seen before include "Flexible container for carrying things" , "Gladstone, for example" , "Claim" , "Pouch" , "Piece of luggage" .)
(Other definitions for purse that I've seen before include "amount of money" , "Prize money - prepare to whistle" , "sometimes with strings attached?" , "Small money bag" , "Pocket" .)