Question

how is the map about immigration,c.1860:(by momus) different from a typical map of the united states

Answer 1

The map replaces the names of states and major geographical areas with names that represent the Irish. This is because many Americans at the time feared the Irish immigrants will  overtake many cities with their culture. ( Please note you did not provide the image of the map, so I can only assume we are talking about the same one.)