IMO...
Pre-Med is a noun representing someone who is studying and taking the appropriate classes with the intention of entering medical school.
"Because I am a Pre-Med I had to take Organic Chemistry I and II."
Premed, on the other hand, is an adjective describing someone with the mindset that so many people aspiring to get into medical school adopt.
"Because I am premed I started freaking out because I got a 89% on my first Organic Chemistry test, and now I'm going to post on SDN asking people if I still have a chance of getting into medical school with such a bad grade on my record."