The first distinction that needs to be made here is the difference between breakbeats as a generic term for a looped drumbeat and breakbeat as used to denote a musical style. We define it here as a style of beats with a lower bpm than drum+bass and with a different style than the so easily recognizable signature of jungle/drum+bass. In simpler terms the breaks played by the pilots are faster than hip-hop, slower than jungle, and pretty damn funky.
Turntablism is a philosophy in of itself, pioneered in part by people like the invisible skratch pickles. This is a philosophy that demands that the turntable be respected as a musical instrument. The abilities of a skilled DJ on the decks could be likened to those of a skilled Jazz improvist, with one exception, any sound that can be recorded can be pressed onto vinyl and become part of a turntablists arsenal. So whereas a trumpet player can play a solo, a turntablist can manipulated a record (or two records, or three, or four etc.) playing a trumpet solo, then cut out a drum solo, or construct both simultaneously. In addition many turntablists can perform at the same time (check out the X-ecutioners) in a truly awesome display of musical power. The pilots hold this philosophy to be the prime directive of personal development in terms of what it means to be a DJ.
What's the difference?
The difference between this and the traditional style of DJing should be noted. A techno DJ, for example, (and this is a generalization and does not apply to all, especially not Jeff Mills) is playing a record of music created somewhere else, then playing the next to keep dancers dancin. With this kind of style (house, techno, trance) the key is a seamless flow, not an easy task and one that takes a lot of hard work to become proficient at. A turntablist takes a record and uses sounds off of it to create a new sound. If you record what he makes and compare it to the sound of the record playing on it's own, It will be almost impossible to recognize the similarity. The turntablist is creating something new