Originally Posted by
Reign
They're basically just alternate timelines. Nasu words it as "they're in their own settings" rather than outright calling it non-canon. By doing so, it feels like he's letting Keikenchi and Hiroyama do what they want but has different ideas for the things they're covering than they do. Like what Comun listed above. His response to Keikenchi's ideas for Oryou (and probably Izanami and Izanagi given Oryou's backstory) was "that's not how it is in this setting but I like it so go ahead", so he's essentially giving them their own sandboxes to write their stuff down, but by sectioning them off they aren't stepping on his own ideas for those concepts. I doubt we're going to see "Oda Nobunaga by Kinoko Nasu!" when Gudaguda Nobu is already well established in real life as The Fate Nobunaga, but it leaves that avenue open.
The most immediately noticeable difference at a glance is Ryouma's and Erice's Ame-no-Sakahokos looking and behaving completely differently.