Difference 1. In a perfectly competitive market marginal revenue is equal to average revenue at all quantity of production and the price for all firms is set at the same value. By contrast, in a monopoly market with a single firm, the firm faces one curve for Marginal Revenue and a different curve for Average Revenue which reflects a higher price for every level of output. The firm will produce at the intersection of the Marginal Revenue and Marginal Cost curves but will set the price dictated by the Average Cost curve.
Difference 2. In a perfectly competitive market there are no barriers to entry or exit which means that firms can come and go freely. The free entry and exit of firms gives rise to a common price and zero economic profits in the long run for all firms in the market. This is because as prices shift to profit-making levels, more firms enter the market driving up the supply and driving down the price. Firms that lose money at the new price then exit the market and the price returns. In a monopoly market, there are very large barriers to entry and exit which allow the dominant firm in the market to make economic profits in the long run.
Similarity: Whether or not a firm operates in a perfectly competitive market or a monopoly market it will set its output at the intersection of the marginal cost curve and the marginal revenue curve. This is the level after which the firm begins to make a loss on each individual unit of production.