Where did the “wheel” group get its name?

The wheel group on *nix computers typically refers to the group with some sort of root-like access. I’ve heard that on some *nixes it’s the group of users with the right to run su, but on Linux that seems to be anyone (although you need the root password, naturally). On Linux distributions I’ve used it seems to be the group that by default has the right to use sudo; there’s an entry in sudoers for them:

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?