The major difference between these two is that oligopolies have to pay attention to what their competitors are doing whereas monopolies only really have to think about their own internal affairs and the wants and needs of their customers.
In a monopoly, there is only one firm that is selling a particular good or service. That firm, of course, does not need to worry about competition. What it does want to do, however, is to ensure that it is making as much profit as it can. When it sets its prices, it will look at its own costs and it will look at what its customers are willing to pay. It will look at its own costs to make sure that it is making a good profit, but it will look at customers’ demand to ensure that it does not set its prices so high that the customers simply stop buying.
In an oligopoly, things are different. Firms in an oligopoly must pay at least as much attention to what their competitors are doing as they do to anything else. They have to monitor any changes that their competitors make so that they can respond to those changes and preserve their own market share.
Thus, firms in oligopoly pay a great deal of attention to competitors where firms in a monopoly do not.