Paper Mario in Mario Land is a known entity in Mario Land, kinda like in Paper Jam, but the storybook Luigi opens up covers the existence of Sticker Star. There are other Paper Mario volumes in the library, and they contain the stories of Paper Mario 64, Paper Mario: Color Splash, and Paper Mario: Origami King. Thousand Year Door and Super Paper Mario are unsanctioned fan works that have a dedicated cult following on the Internet but not really known in the general public.
Paper Mario does exist separate from Mario. While he can vocalize, he has severe tongue issues from flawed paper rendering, making him mute, so he communicates fluently in sign language (when Olivia was around, he had to be careful he didn't accidentally activate the 1,000 Fold Arms while communicating). He's even more polite and naive than flesh Mario, but he's not as much of a dork as flesh Mario. He's an good, eloquent writer himself, and he's the one who provided all the Museum plaque descriptions and he wrote the amusing, slightly sarcastic in-game descriptions in
Sticker. The description for Squirt Gun, for instance?
In its current state, this liquid launcher is but a memory of wars long past. But load it with water, and it becomes more terrifying than you can imagine.
He actually wrote that.
If flesh Mario (and probably Luigi) transported to the Paper Mario world, he'd retain his blue eyes, he'd retain the smaller stache, and he'd have his legs. He'd have a visible mouth. Needless to say, he looks more like on-model Mario.
Paper Luigi is much different than flesh Luigi, though. Paper Luigi is much more sarcastic, quippy, and arrogant. He is also a bit more lazy, though he's quite good at organizing parades such as the Thanksgiving Day one when Mario is out. To be fair, unlike flesh Luigi, Paper Luigi has never really been on any real adventures so he's probably has a lot of pent up bitterness, though nothing truly ill will for Paper Mario. However if you're nice to him he'll tell you why Paper Mario has developed muteness.
Paper Bowser is seen as a once threatening villain but he lost a lot of bite after the events of the first volume, and so he generally is much more of a threat when there's external forces corrupting him, see black paint and sticker shenanigans. He doesn't understand sign language very well, so he usually misunderstands Paper Mario's commands and assumes Paper Mario is okay with the kidnappings. Attempted kidnappings anyway.
Paper Peach is not all that different from flesh Peach but, she's much quieter than flesh Peach, and she lets most of the Toad administration do the work for her. She's even more vulnerable than flesh Peach since the universe still hasn't caught up to the idea that maybe she should be a supporting protagonist and not a damsel in distress. She has no idea Princess Daisy is an actual thing, but she's fantasized about having a sister. She loves cooking even more than flesh Peach, having learnt her techniques from Tayce T. (who speaks in a southern accent). Everyone seems to have learned bit from her, even Paper Luigi. If Paper Peach wasn't kidnapped and possessed that much, Paper Mario would eventually catch up one day...