Is the Moderator usergroup togglable on Discourse?

So, our Discourse forum has Admins and Mods, right? But when checked about the official Discourse Meta, they only have Admins. On our forums, mods got the shield icon next to their nickname, admins got nothing. On Discourse Meta, Admins got the shield icon.

So, now I’ve been wondering: Is the Mod usergroup something which can be toggled/added?

You can add or remove usergroups, yes.

And the icon you get for being in a usergroup can also be determined, am I right?