Most demoscene music is characteristic in that it's made by hand, distributed as semi-open source, and executed in real-time. Composers adapt to the technical limitations as well as the cultural conditions, where resources were often reserved for the visual content. For these purposes, demosceners refined the tracker-software, which is essentially a text-based step-sequencer with quick access to all sound parameters.
The Amiga 500 (1987) was the first home computer that you could make chart hits with. The megamix was a popular form in the scene [see clip above] but used too much memory for demos. The so-called 'ST-01 style' used smaller samples bundled with the Soundtracker software. In 1989, 4-mat cut out snippets of these samples and looped them, to make beeps. The term chipmusic was coined for this music, which flirted with C64-aesthetics and had a file size of about 15 kb, which made intro-coders happy.
Meanwhile, several e.g. C64-musicians were striving away from 'chipmusic' towards e.g. industrial/rave, in line with the demoscene desire for transgression. Some tried to mimic older styles such as jazz and funk  and what was known in the demoscene as 'doskpop' - something inbetween Jarre and Laserdance, very popular in the early 1990s demoscene.
On the PC, demos became more similar to music videos or media art and some demoscene musicians were signed to labels (e.g. Brothomstates on Warp). Demos started to use MP3-audio, while other composers (again) preferred more restrictive settings like soundchips and tiny soft-synthesis.
The musicdisk is an emblematic artifact of demoscene music. It's an executable file that contains music, graphics and texts generated in real-time. The songs are not linear recordings from A to B, but often contain loop-points so they can be heard forever. A more obscure artifact is the tracker animation, that turns the score into an animation.
 Amegas by Karsten Obarski (Amiga Mod, 68kb, 1987)
 Paul the Penguin by Radix (Amiga Mod, 22kb, 1996). [On YouTube]
 Doskpop-mix by Random (MP3, 2009)