Sudo is a setuid binary, which means it executes with root permissions as a child of of the calling process. This technically works, but gives the untrusted process a lot of ways to mess with sudo and potentially exploit it for unauthorized access.
Run0 works by having a system service always running in the background as root. Running a command just sends a message to the already running seevice. This leaves a lot less room for exploits.
Because the thing people refer to when they say “linux” is not actually an operating system. It is a family of operating systems built by different groups that are built mostly the same way from mostly the same components (which, themselves are built by separate groups).