I think the question is clear in the attachment. Is there any difference if I choose to setup the Anonymous Access using the Group permission over the setting of Anonymous Access at the bottom?
The permissions under Anonymous Access is the real permission set that anonymous users will be affected by. The group 'anonymous' is a group created by an admin on your instance and doesn't reflect the real permission set for Anonymous users to the site. I don't see why a group was created for anonymous users in the first place (since they have to register to be part of a group and at that point are no longer anonymous).
https://confluence.atlassian.com/display/DOC/Setting+Up+Public+Access
No, the 'anonymous group' is not a default group in Confluence. You can't assign anonymous users to a group, since only registered users can be assigned a group.
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