Why is the ‘sudo’ password different than the ‘su root’ password

On my personal machine, I often type sudo in front of certain commands in order to accomplish administrative tasks. I had hoped to avoid doing this throughout the day, by typing su root and providing the same password I usually do for sudo. However, the two passwords are not the same(I don’t know how to log in to su root). Is running a command with sudo different than logging in with su root and running the same command?

using sudo on GUI applications

When I was using kubuntu, I could always open X applications with sudo, sudo kate for example. Now that I’ve switched to arch that doesn’t work. I know I’ve always been told to use kdesu, but what setting is there in kubuntu that lets me use sudo on X apps that prevents me from doing it on arch?