Modern dance is a type of dance that is considered to be very random. Some dancers create their steps based on what they feel will fit well with the beat of the song. Modern dances usually make use of the core and the torso. Contemporary dance may be a mixture of the different dances right now that are considered to be collaborative.
For example, there are a lot of groups that make use of both jazz and ballet or ballet and interpretative. They usually feel that the mix will allow the dance to have different twist while staying true to the original form. Both types of dances are very interesting.