Rockabilly was originally just a genre of music which mixed Rock-N-Roll and HillBilly Country music.  Rockabilly groups stood out by sporting Country Western attire, rather than a suit and tie like a mainstream group would wear.

The music died out in popularity pretty quickly but made a resurgence in the 1970s and has carried through to today.  Those who listen to and party to the sound have formed an entirely new clique using the name of the music, ROCKABILLY.  Sooooooo... Nowadays here in the US, those who admire the era of the 1950s are ROCKABILLY.  If you grease your hair back, have a number of tattoos, act like a hooligan, pimp your ride with flames... then you could call yourself a Greaser.  If you grease your hair back, but you just admire the 1950s without the distain for social inequalities then you are Rockabilly.  I hope that makes sense.  Of course, it seems that those definitions change somewhat depending on what country you're in, and Rockabilly is still a popular clique in several areas around the world.