If you’re wanting something content-agnostic (for games, movies, music, etc) then what you’re probably looking for is an ISO maker. What it does is makes a full copy of the disc and saves it as an ISO - an ISO being a virtual disc image. You can then mount the ISO image as a virtual drive (it will function identically to a real drive with the disc inserted), or you can use the ISO to create a new disc using programs for each (note: it won’t save the graphics on top of the disc, just the data on the disc).
I’m not sure what the commonly used FOSS tools are for that kinda thing (I think most Linux distros have mounting/unmounting ISOs built-in), however imgburn is generally considered to be pretty good for creating ISOs and burning them to discs. The one catch is that I’m not sure how well it handles copy-protection schemes like what’re on Blu-ray. Additionally, when it comes to mounting ISOs, I’m not sure what most people use but I’ve personally used WinCDemu for that on windows, but there may be better tools available.