Board Thread:Boruto: Naruto the Movie/@comment-1512913-20160326012154/@comment-734582-20160402140754

Elveonora wrote: Kishi hasn't made the doujutsu situation any easier... I'd love to see him make a definitive explanation of Dojutsu... but sadly that'll probably be a pipe dream forever.

I think you're mostly correct, but i also have some additions:

Hagoromo's Rinnegan are Kekkei Mora. What sets them apart is apparently the ability to pull souls directly from the afterlife, All Creation, and the ability of Transmigration. Asura and Indra could not fully access this power, only Black Zetsu's machinations made their feud strong enough to transcend time.

Kaguya's Byakugan are Kekkei Mora. it's not clear what's different, but it's my belief that a Pure Byakugan has no blind spot. Or simply, the less pure a Byakugan, the bigger the blindspot. Following that train of thought, it's possible the original Byakugan wasn't that special an eye until Chakra unlocked it's potential (e.g. the ability to emit chakra from all tenketsu).

Rinne Sharingan is essentially the ultimate form of the Sharingan. The Sharingan possesses power over the connection between reality and fantasy, the Rinne Sharingan does so to the ultimate amount (it overwrites reality).

Rinnegan is a specialization of this power, applying the Sharingan's powers to Life and Death. It seems to have a power the Rinne Sharingan does not (the ability to interact with the soul) while lacking the reality-overwriting powers of the Rinne Sharingan.

Sasuke's Rinnegan is simply a merger of a Rinnegan and a Sharingan. This obviously makes it closer to a Rinne Sharingan (as evidenced by his Spacetime Ninjutsu) but not actually a Rinne Sharingan (as evidenced by the lack of such things as Infinite Tsukuyome).

As to Kinshiki and Momoshiki, both the book and the movie imply that they turned their Chakra Fruit into the edibles (and planned on doing it here as well, which is why Kaguya was forbidden to eat it). This has given them some permanent powers (e.g. the rinnegan or weapon creation) but not fully. Kinshiki's comments suggest that Momoshiki and Kinshiki themselves aren't the treat Kaguya faced, but rather their predecessors were. Furthermore, parts of the fruit were probably lost which is why they do not have Rinne Sharingan.