Problem scenario
You have seen Linux distributions use wheel whereas some use admin. What is the difference?
Solution
For most purposes, there is no difference.
Many RedHat distributions use wheel (per page 429 of Fedora and RedHat by Sobell).
Ubuntu uses wheel (per this posting).
To add a Linux user to a sudoers file, see this posting. For the correct command to modify the sudoers file, see this posting. If you want to learn about how to modify the sudoers file, see this internal posting. If you need help troubleshooter a modified sudoers file, see this internal posting.