I'm familiar with three major disk-based copy protection schemes from the 2000s. Interestingly they all begin with S: SafeDisc, SecuROM, StarForce.
SafeDisc and StarForce are implemented using low-level boot-start drivers. The one for SafeDisc (secdrv.sys) has been shipped with Windows, and is present in all versions, including Windows 10, but in Windows 10 it's forced-disabled and the service simply refuses to start even if you try to do so manually. There may be some unofficial hacks to force it to load regardless, but I'm not familiar with those. On Vista, 7, 8.1 - you can simply not install the patch that disables it, and SafeDisc games continue working.
StarForce drivers typically shipped with the games, and the company provided utilities for end-users to
update or remove their drivers. Unfortunately, while later version of StarForce run on every Windows up to 10, early versions do not, and if a game executable is locked to a particular driver version that is too old, you are stuck.
As far as SecuROM goes, I'm not fully aware about how it works, but
their FAQ claims that they use no driver, and no kernel-level component at all. This is probably while this scheme can more easily be circumvented by various utilities, and because of that SecuROM-protected games often refuse to load at all, if they detect specific programs running, such as CD drive emulators, or even Process Explorer (weird, huh?).