It's an off-shoot. From "You Will Be Okay", there's at LEAST 7 rings, per Stolas. They mention the rings again in HB Ep. 3 when Blitzo says that the nearest ocean is '3 rings down'. If Viv is using the full 10 rings as her guide, then that would make the plane that HB and ostensibly HH takes part in Circle II: Lust, which obviously checks out. Three rings 'down' from that is Circle V: Wrath, where the angry are basically 'drowned' for eternity in the river Styx. This would be the only Circle that could be both where an 'ocean' could be, while still being "three rings down" from another Circle.
Now, the only question is, was Stolas correct in saying that Viv's Hell only has 7 Circles, or was this just part of a bedtime song, and the full 10 exist? If it's the former, which three were removed?