@FAST6191 - in general properly-said saves are not shared, however some games have what most people would call "main save" (or other useful stuff) in extdata, and that is definitely shared
As for the "mod", a modified cia would of course not apply, but a Luma overlay would - after all, it goes by titleID
Of course, you could always disable that feature in Luma's settings, or use games of different regions, or change the game's titleid (unreliable across games, especially Pokemon hates it)