DVD’s and CDR’s are completely different. You can scratch a label on a DVD with a screwdriver and not harm the discs at all. (yes, I’ve done it).
CDR’s are made differently, and the back side is the vulnerable side. There were some reports in years past about “solvent-based” markers that were dissolving the lacquer that protects the reflective layer on the back of the CDR, and thus rendering them unreadable. Thus it’s important to know what “solvent-based” really means. Generally, “solvent” refers to petroleum-based chemicals like paint thinner. A few permanent markers do use solvents to suspend the dye.
Sharpies mostly use alcohol, which although is chemically referred to as a solvent, (as is water), it is not of the class of chemical solvents that eat lacquer or plastics. Sharpies also offer the benefit of being semi-permanent, but can also be removed with alcohol if you want to re-label. They are harmless to plastics and to lacquer.
So you can write on a DVD with anything you like, short of a blow-torch or dremel. On CDR’s just use alcohol or water based markers and you are fine.