The Immortal Ring Realm and the Connecting Heaven Realm were tied by a strong tether.
Usually, just the 'Connecting' portion of the latter realm was emphasized. This was the process of running one's energies through one's Pulses and Vessels. It was this connecting that formed the 'Ring' of that would thus be nurtured during the Immortal Ring Realm.
This was where the differences of the Immortal Ring Realm stemmed from.
A mediocre cultivator might not open all of their Pulses and Vessels. They might also potentially enter the Soul Birth Realm prematurely, thus losing access to a perfect foundation.
Those who lost a chance at this perfect foundation would have their Immortal Ring Realm broken up into Lower, Middle, Upper and Peak. This more 'general' separation allowed for more fluidity and was less hard-lined in comparison to higher forms of the Immortal Ring Realm.