As pwc101 said, su requires the root user password and sudo requires a regular user password. What you can or can't do with sudo, depends on how you set up your sudoers file. Some distros (no finger-pointing) do this:
# User privilege specification
regular-user-name ALL=(ALL) ALL
That gives that regular user full root power. However, you can define it in a much more specific way, and at many levels. Check man sudoers
for all the gory details.
By the way, I strongly recommend that you never edit /etc/sudoers directly. Use the wrapper visudo
instead - if your system has it. It prevents you from saving the file if there are syntax errors, which is useful.