There are just two fixed groups of users in unix-derived OSes: the superuser (root) and ordinary users (all the rest).
Assigning group ownership to device, program and data files and assigning users to appropriate groups, one (the superuser, of course) can granularly define who can mount/unmount permanent and removable storage, access sound and video subsystems, scanners and printers, open or close networking connections, etc, etc...
There are some predefined groups (adm, wheel, disk, audio, cdrom, lp), but one can drop them and use any other self-created and self-named groups. They are created by groupadd and manipulated by groupmod, users are assigned to the appropriate groups in time of their creation by useradd and at any other time by usermod (see man pages for these commands)
Hope this helps,
Many *nixes offer Role Based Access Control which adds more flexibility to "types" of users since you can define "Roles" that people can belong to, each role having granular access to certain things. You can also use SELlinux whcih offers even more granularity and control.