While not a formal essay, this post is about MN 34 and the Pali term ‘para loka’ found therein.
MN 34 says:
There are ascetics and brahmins who are skilled in this world (imassa lokassa) and the other world (parassa lokassa), skilled in Māra’s dominion and its opposite, and skilled in Death’s dominion (maccudheyyassa - refer to Iti 59) and its opposite.
MN 34
The above statement appears to equate “the other world” (“para loka”) with “Mara’s opposite” and “Death’s opposite”. Therefore, the term “this world” (“imassa loka”) appears to equate with the world/dominion of Mara and Death.
MN 34 continues to say:
Just like the bulls, fathers and leaders of the herd, who crossed the Ganges to safety are the mendicants who are perfected, who have ended the defilements… are rightly freed through enlightenment. Having breasted Māra’s stream, they have safely crossed over to the far shore.
Just like the strong and tractable cattle who crossed the Ganges to safety are the mendicants who, with the ending of the five lower fetters, are reborn spontaneously. They’re extinguished there, and are not liable to return from that world (tasmā lokā). They too, having breasted Māra’s stream, will safely cross over to the far shore.
Just like the bullocks and heifers who crossed the Ganges to safety
are the mendicants who, with the ending of three fetters, and the weakening of greed, hate, and delusion, are once-returners. They come back to this world (imaṁ lokaṁ) once only, then make an end of suffering. They too, having breasted Māra’s stream, will safely cross over to the far shore.… the mendicants who, with the ending of three fetters are stream-enterers, not liable to be reborn in the underworld, bound for awakening. They too, having breasted Māra’s stream, will safely cross over to the far shore.
… the mendicants who are followers of teachings, followers by faith. They too, having breasted Māra’s stream, will safely cross over to the far shore.
Mendicants, I am skilled in this world and the other world, skilled in Māra’s dominion and its opposite, and skilled in Death’s dominion and its opposite. If anyone thinks I am worth listening to and trusting, it will be for their lasting welfare and happiness.
That is what the Buddha said.
Then the Holy One, the Teacher, went on to say:
“This world (ayaṁ loko) and the other world (paro loko) have been clearly explained by one who knows; as well as Māra’s reach, and what’s out of Death’s reach."
MN 34
Suttas such as SN 12.44 say the world originates from craving. DN 15 describes the deadly worldly conflicts caused by craving. Dhp 167–178 speaks in negative ways about ‘the world’.
Dhp 44–59 refers to how a trainee will discriminate (vicessati) the world of Yama (Yamaloka), cutting off Māra’s blossoming (sensuality) and vanish from the King of Death (maccu rāja). Dhp 44–59 is using terms very similar to MN 34. Dhp 44-59 also refers to how the terminator gains control of the man who has not had his fill of sensual pleasures (atittaññeva kāmesu antako kurute vasaṁ).
Iti 96 defines a returner as returning to sensual pleasures. AN 7.15 refers to the returner crossing over to the other shore; but then returning.
Based on the above, the impression from MN 34 is:
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The term ‘this world’ (‘imassa/ayaṁ loka’) refers to the ordinary world of craving and sensuality; and that the once-returner returns to this world.
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The term ‘the other world’ (‘para loka’) refers to a higher world superior to the ordinary world of craving and sensuality; and that the non-returner fully attains this ‘other world’; never returning from this ‘other world’.
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Although not all of the mentioned strata of the Buddha’s disciples have crossed to the other shore (Nibbana), MN 34 appears to say all true disciples to some degree have escaped from or have a perspective on Mara and Death. All have “breasted Māra’s stream”. Therefore, all of these disciples (except Arahants because Nibbana is not ‘a world’) abide in various degrees in ‘the other world’ (‘para loka’), i.e., a different (mental) world to the ordinary sensual material world. Note, for example, MN 79 describes the four jhana as ‘a world of only happiness’ (ekantasukho loko).
What do we think about this? 
“Whoever has well developed
“Sīlaṁ samādhi paññā ca,
ethics, immersion, and wisdom
yassa ete subhāvitā;
has slipped free of Māra’s dominion
Atikkamma māradheyyaṁ,
and shines like the sun.”
ādiccova virocatī”ti.Iti 59