Dorayaki
King Bowser
As we knew from Paper Jam, the OG and Paper stories are two worlds, with Paper being the storybook version of the OG. However, sometime ago I also see some opinions that say Paper Mario is entirely seperate from the main Super Mario series thus OG or Paper world doesn't share contents from the other series. Altho there is Super Mario Kun which integrate PM stories as part of mainline, Nintendo don't seem to consider that as canon.
Personally, I don't think there is official evidence of difference since chances are the characters just mostly don't talk about it directly in games, and that wouldn't cause direct conflicts in stories or canon (e.g. Paper Florian and Flower Kingdom exist in Paper World, just they don't show up and nobody ever feel the need to mention them.) Of course, no evidence for being entirely identical either way so we don't have clear answer for now until official reveal. In series history Star Spirits were the only Paper characters that make canon appearances in OG world, and Nintendo have been very passive in showing any Paper contents in mainline games or major media like the Illumination movie series.
While it's understandable for NIntendo to not easily mention RPG contents due to having trouble with controlling the recurring contents in main series, plus that Nintendo have no budget to do more 3D renders, as a Paper fan I sure wish to see Paper contents acknowledged as mainline canon and wish that they at least mention each other more often.
Which theory do you think Nintendo / Miyamoto stans? And which theory do you personally stan?
R: The first 3 games absolutely happened in THE Mario world, and that is the version we see. The "Paper Mario Style" is a stylistic choice for presenting it to the player, and all paper elements in gameplay are explainable via magic. The modern trilogy as we see them are most likely in a separate world, possibly the one from Paper Jam but i really don't care enough about Paper Jam to definitively decide on that. But their events in some form or another most likely did happen in the main world, we just didn't see it.