The difference between these two demand curves is that the demand curve that faces a monopolist slopes downward. By contrast, the demand curve that faces a firm in perfect competition is flat. This reflects the natures of the two market structures.
In perfect competition, the firm is a price taker. It produces a homogeneous product and therefore cannot charge any more for its product than any other firm. If it charges a higher price, it will not be able to sell any of its product. Therefore, its demand curve is flat.
In a monopoly, the demand curve slopes downward. This is because people will buy less of the goods that the monopoly produces as the price of the goods rises. The curve may be very steep, assuming that the good is relatively necessary to people and therefore has inelastic demand, but it does go downward. People actually will stop buying as much of the product as the price rises.
Thus, the demand curve for a firm in perfect competition is flat while the demand curve for a monopolist slopes downward.