The expression originates from a policy of tax collection devised by John Morton, Lord Chancellor 1487, under the rule of King Henry VII. His approach was that if the subject lived in luxury and had clearly spent a lot of money on himself, he obviously had sufficient income to spare for the king. Alternatively, if the subject lived frugally, and showed no sign of being wealthy, he must have had substantial savings and could therefore afford to give it to the king. These arguments were the two prongs of the fork and regardless of whether the subject was rich or poor, he didn't have a favourable choice.
"Morton's Fork Coup" is a manoeuvre in the game of Bridge that uses the principle of Morton's Fork.