Temporary bans can only handed out by theymos or me, others request them as needed in the staff forum. Stefan (justmoon) can but typically doesn't.
Global moderators can ban (permanent), ip-ban, nuke, whitelist.
Local (board specific) mods can nuke, whitelist.

Nuke removes all of a users posts/threads and bans them (spambots).
Whitelist used to allow a newbie to post outside the newbie forum, now it reduces the time restrictions between posts.
If the local mods need someone banned they request it in the staff forum where it's vetted and approved/denied.
There are also patrollers who can moderate all newbies regardless of what board they are posting in.

The autoban thing is misleading. The message you got when banned by a global mod used to include autoban in it, but that was just the name of the tool (and the usergroup), there are no autobans. That message has since been changed.