Are modern and contemporary dance the same thing? And if they are not the same what is the difference?

It would appear that Modern and Contemporary Dance are not the same thing. From the following site: Contemporary dance - Wikipedia, the free encyclopedia

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Contemporary dance is the name given to a group of 20th century concert dance forms. It is a collection of systems and methods developed from Modern and Postmodern dance. Thus contemporary dance is not a specific dance technique.

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You might like to check out the other information that is available also on the referenced site above.