Droid is the name of the phone. It runs Android, like many other phones. The only difference is its the only phone right now to have 2.0. I didn't buy mine for the software. I bought it because is supposed to be a kickass phone, which it is so far.
I played with the non working one at Bestbuy and didn't like it much. I made them get out the real one and it was a big difference.