The various types of market structures vary along three dimensions. Monopolistic competition and oligopoly are always different in two of these dimensions and sometimes different in the other.
One dimension is the type of product that is sold. There are times when companies in these two market structures sell the same type of product. Firms in monopolistic competition always sell differentiated products. These are products that can be made to seem different from those sold by another firm. Firms in oligopoly sometimes sell differentiated products, but they also sell homogeneous products (ones that are identical regardless of which firm makes them) at times.
Another dimension is the difficulty of entry into a market. It is easy to enter a market that is in monopolistic competition. It is difficult to enter a market that is in oligopoly.
This leads to the third difference. In an oligopoly, there are very few firms. The market consists of a few very big firms. By contrast, there are a very high number of firms in monopolistic competition.
Thus, these market structures vary in two or even three ways.