What is the difference between a Cournot and Bertrand competition?

Bertrand Competition:
Is a Model were firms compete on price, which naturally triggers the incentive to undercut competition by lowering price, thereby depleting profit until the product is selling at zero economic profit. This effectively is the pure-strategy Nash equilibrium.

Cournot Competition:
Is a model (Oligopoly the model was built on Duopoly) where a firm competes in the Oligopoly market on quantity, maximizing profit given what it believes the other firm(s) will produce. Profit for the firm is maximized by setting its marginal revenue equal to marginal cost and determining it's quantity relative it's rival. There is no competition on price here.