Think of Silicon Carbide as sand paper, you're filing the surface of whatever you're polishing with silicon carbide grains of specific sizes (the grit size). The grit is fully exposed - hence they'll work on pretty much anything.
Diamond pads (excluding electroplated and vacuum brazed types) are generally resins cast in a mould mixed with diamond dust/granules and allowed to cure. When the diamond resin pad is introduced to the product it's polishing, the resin wears on the product, exposing diamond, which does the polishing. It's important the resin is formulated for the product being polished otherwise it just won't work.
A dry diamond pad designed for polishing granite or concrete won't work on Limestone, the limestone simply isn't abrasive enough to wear the resin to expose the diamond, so what tends to happen it it just rubs the surface of the stone, creates heat and eventually starts to melt the resin, that's where you get brown resin transfer stains.
The flip side is a resin diamond pad designed specifically for soft product like marble or limestone will simply wear away in no time when used on something more dense or abrasive.
There's also no such thing as a diamond pad that's truly wet & dry use, it's one or the other.
Manmade quartz is a difficult product to polish dry, really only silicon carbide is appropriate for edge polishing (dry) but then there's the question of if the dust is harmfull. Diamond pads are only really appropriate used wet as the abrasion of the pad can often generate enough heat when used dry to melt the resin content of the quartz (more brown smears).
Don't try to surface polish quartz, it'll generally cause more problems than it will solve, it can be done but it's a specialist operation.