Difference between Stalemate, Impasse and Mexican Standoff

The Big Bang Theory's Sheldon explains:

Sheldon: "In chess, a stalemate refers to a situation in which there are no remaining moves. You have plenty of moves available. You could beat us up and steal the money, you could kill us … really, you’re only limited by your imagination."

Dangerous liquid-helium dealer: “Huh. All these years I’ve been using ‘stalemate,’ when I really mean ‘impasse.’ I feel foolish”
....
Sheldon: "The essence of a Mexican Standoff is that no one can walk away from a conflict without incurring harm..."

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