No I do not per se think they are on the same planet. At best they share universe, being different planets in a galaxy or something like that. However, there is a side project on the discord which aims to merge all crossover'd nintendo franchises (Mario&Co, Zelda, Kirby, F-zero, Metroid, Star Fox, Splatoon, Starfy). This connected universe has even more ambiguous lore than mario, mind you:



The only thing we can say for sure, if we run with this side project, is that all mario games takes place in one of the branching timelines post OoT. I would argue that it cannot be the Child timeline, due to there simply being too little evidence that any mario games ever crossover'd with the games therein. Regarding the adult timeline, Mario Kart 8 Deluxe might hint that the flood took place if we merge splatoon's flood into it.



However, I would argue given the facts that if Mario shares universe with Zelda, then his games takes places during the Downfall Timeline, around the time of a Link to the past: Mamu/Wart interacts with both protagonists, the OoT-remake no longer has portraits of Mario & co, the Hero of Legend (Link) ends his games after the OoX games traveling the world, and he is known by Cranky, the Brothers Bears in DKC3, and appears in SMRPG.



But in all fairness, given opposing lore and interdimensional travels being a thing in both franchises (Termina/Lorule/Light World/Super Paper Mario) I officially believe that Mario and Zelda occupy different universes that are linked by portals.