Boog as defined from the source, is a type of "feel" or "flavor" when one dances. Also, Boog is an actual dance style(not a series of moves, but a continuous dance style). You don't have to roll everything at once, but more so being very patient with the music, and having that "feel". Boog is different from Boog style. Boog is a "feel" and an actual style. Boog style is when you still have the Boog "feel" but you are adding other styles in with it.
Boog: Patient, funky, smooth, simple movements yet dancing very complimentary inside the music.
Boog style: The same "feel" as mentioned above doing scarecrow, robot, and rock waves.