There is a ‘special admin’ role as well who can do a couple of extra tricks. In the guide it’s referred to as Developer:
I’m not sure why system is both. An admin should be able to do everything a moderator can. Maybe it’s just to cover all the bases and make double sure they can really do everything. 
But for the ‘special’ admin/first admin created along with the site - I think that used to only be granted the admin role, but this was changed to add the mod role too. I believe it was something to do with sites more likely to have only one person running the place in the beginning and auto-adding the mod role makes sure they don’t miss any of the mod notifications.