At the  Cournot model  the two firms "play" at the same time, each knowing the other's reaction curve. In this way, Cournot equilibrium will occur when the curves equalize. That is, a quantity supplied by firm 2 , which causes a quantity supplied response by firm 1 , which, in turn, generates the same quantity supplied by firm 2 initially - so it is a very classic Nash equilibrium. In the Stackelberg Model  the lead firm has an advantage over the follower firm: it sees the follower's reaction curve and chooses a point on that curve. That is, the leading firm will offer an amount X already knowing the reaction of the follower curve, in order to maximize its profit.