What's difference between group admin and adm?

The adm group is only good for viewing all the log files in /var/log (which historically used to be called /var/adm). It has no relation to sudo or root.

Admin is just wrong, it's probably there as an example. Adm is a historical artifact. You can see if either group exists on your system and if there are files/directories owned by them. There may also be PAM (limits.conf) rules.

They are nothing magical. They are just normal groups that may or may not be used in some config or filesystem permission.

You can have a look at Securing Debian Manual for explanations to some of the names. If Ubuntu has a matching one, you might want that instead.

The admin group is used to grant sudo access on ubuntu 11.10 and earlier.

You may also see it on 12.04 for backwards compatibility if you upgraded. If you did a fresh install you will probably not see it.

<= 11.10 use group admin

>= 12.04 use group sudo

Up until Ubuntu 11.10, administrator access using the sudo tool was granted via the "admin" Unix group. In Ubuntu 12.04, administrator access will be granted via the "sudo" group. This makes Ubuntu more consistent with the upstream implementation and Debian. For compatibility purposes, the "admin" group will continue to provide sudo/administrator access in 12.04. [1]

As was mentioned above, adm is related to log access:

adm: Group adm is used for system monitoring tasks. Members of this group can read many log files in /var/log, and can use xconsole. Historically, /var/log was /usr/adm (and later /var/adm), thus the name of the group. [2]

[1] https://wiki.ubuntu.com/PrecisePangolin/ReleaseNotes/UbuntuDesktop#PrecisePangolin.2BAC8-ReleaseNotes.2BAC8-CommonInfrastructure.Common_Infrastructure

[2] https://www.debian.org/doc/manuals/securing-debian-howto/ch12.en.html