The pads also differ by the alloy from which the baseplate is made: steel, aluminium, titanium, carbon, etc. Again, for our bikes, take any — if you just want to ride, rather than become a braking pad sommelier.
As far as rim brakes, the pads are different for aluminium and carbon rims. Pads for aluminium melt if used on carbon. And if not new, they are likely contaminated with metal particles that will quickly wear out the carbon. And pads for carbon just don’t perform well with aluminium rims.
3. Compatibility with brake discsThat’s also simple — normally discs are compatible with any type of pads. There exist (very cheap) discs made of soft alloys that are officially compatible only with organic pads, since metal pads are too aggressive and will ruin the surface. I wouldn’t use that suboptimal kind anyway.
There are a couple more things about discs in this blog here and
there. By the way, on the
main page of the blog there is a convenient search by keywords: you type in, for example, “pads” or “brakes” — and it will find for you all the mentions in all posts. Use it for your reference.