How are oligopoly and monopolistic competition alike and how are they different?

There are both similarities and differences between these two market structures.

The most obvious difference is in the number of firms involved.  In an oligopoly only a few firms are in the market.  By contrast, many small firms are involved in monopolistic competition.  An oligopoly is generally considered to consist of between two and twenty firms.  The lower number is set, but the higher number is not -- there is no firm number of firms that separates oligopoly from monopolistic competition.

Another major difference is that firms in oligopolies affect one another.  Price changes (for example) by one firm will affect the choices of other firms.  This is not the case in monopolistic competiton.

The main similarity is in the kinds of products firms in these two market structures produce.  In both, the firms can be producing differentiated products (although some oligopolies are producing homogeneous products).