All characters evolve over time if they are given enough appearances, both in gaming and outside of gaming.
Consider Mickey Mouse. His appearance has changed from the early cartoons, and not just because the original Mickey was black and white. He gained pupils around the time of Fantasia, has been portrayed as a 3D model, and even looks different in the theme parks (where he wears a bowtie for some reason).
Mickey's personality has changed depending on which media you see him in. He's more mischievous at times, but when Donald and Goofy are in the same cartoon, he's actually the boring one most of the time. Sometimes, he has more spunk, sometimes, he's more a leader--yet at the end of the day, it's the same guy.
Mario is practically the Mickey of the video game world, so it would make sense to adapt him a bit for different scenarios.
Other characters have more inconsistencies. Ever notice how Koopa Troopas can be on four legs or two, even after there was no excuse to be made for the limitations of a gaming system? Why does Princess Peach have a ponytail in Mario Kart but not Smash, where it would seem advantageous to have one? What is with Luigi's voice changing and being high-pitched in some N64 games but deep in others?
I know I may be overthinking this, but I figured I'd put some thoughts out there.