Answer.com has some good information about modern dance, postmodern dance, and contemporary dance.

You make some excellent points about a very confusing topic. The current dance atmosphere is quite eclectic and there are no clear lines separating the genres that once existed. It helps to understand that while Modern Dance may be classified according to established techniques, Contemporary Dance is classified by its choreographic processes.

The concept of contemporary dance is especially hard to explain to students who have little experience with concert dance yet have competed in the "modern" or "contemporary" genres. Since many of the dancers do not actually study modern dance techniques or engage in a choreographic process, I consider what they are performing to be an "interpretaion" of those forms. It's the look without the process, kind of like when a comedian does an interpretation of a celebrity. I suppose that this has some value to the dancer, just as any recital choreography would. However, I believe it's important for dance educators to 1) know the difference and 2) pass this knowledge along to their students. Help them to understand the history of contemporary dance art and how what they are doing is different. I wrote a nutshell history in a post here at Dancer Universe and on my blog called, "What Is Modern Dance?" I hope it will encourage students to look deeper into the legacy of dance.