If you have created a new account, or just logged into your Linux Distribution you may not be able to use the sudo command. This is because the account is not in the sudoers file. I am going to go over how you can add a user to the sudoers file, either by using the usermod command, or by manually editing the sudoers file.
The options you mean are arbitrary. You can use any group name you want for sudo privilage, or just directly add the user(i use wheel group personaly). Also if you are interested you can look at doas which is like sudo but a simpler config file.
wheel group looks BSD history style (wheel group is used on BSD to allow normal users to use the su (yes, su) command). On my Arch Linux based distribution I see both wheel and sudo groups mentioned when I use the visudo command, but only the wheel group exists, not the sudo group. That looks a little bit sloppy from Arch Linux maintainers one could argue, only copying a very broad manual page style sudo config file. Yes, OpenBSD doas has some people enthusiastic over the years, and it is ported for use in Linux. I’ve played with doas last year but for now I’ll stick with su and sudo. Yesterday I read about please as sudo alternative. https://aur.archlinux.org/packages/pleaser/