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.

"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] wiki.ubuntu.com/PrecisePangolin/ReleaseNotes/UbuntuDesktop#PrecisePangolin.2BAC8-ReleaseNotes.2BAC8-CommonInfrastructure.Common_Infrastructure

[2] www.debiandotorg/doc/manuals/securing-debian-howto/ch12.en.html"