It's been discussed here before... really there is no more difference than that between drivers and motorists, both being the same. "Bike riders" is the term often used for people casually riding bikes, perhaps not cognizant of the rules of the road for cyclists or of their rights, and may meander from sidewalk to street to path. "Cyclists" is a term often given to those that think themselves superior users of bicycles... perhaps aware of the rules, but more often exerting themselves in a physically meaningful way and perhaps even asserting their rights... but the fact is we are all "brothers and sisters" on two wheels.
Just because one wears lycra and bright clothing that doesn't really mean a thing... some of the most astute members of the cycling community wear shorts and a baseball cap, and "wanna be Lances" can put on a jersey just as easily as anyone else can wear a Raiders shirt.