There are multiple differences, of course, especially since Genos undisguisedly looks up to Saitama, even to the point of moving in with him. ("Absolutely not," Saitama says. "Oh, you'll pay rent. Gotta toothbrush?")
But the major difference, to me, is something inherent to the manga and anime, namely, neither Genos or Saitama are expected to do everything, not even Saitama.
That is, Saitama is limited in one very important way: he can only fight where he is, when he is, and if he knows about the threat. When the arena gets invaded by monsters, Saitama is in the bathroom. He gets out only after Suiryu is practically pulverized.
The reality here is also true with Superman & Batman. Lois & Clark has a decent episode in which Lois, temporarily a superhero, gets upset when she realizes that stopping to help in one crisis will prevent her from helping in another, no matter how fast she is.The difference is that One Punch Man assumes that of course, heroes can't be everywhere at once. When the alien ship comes to conquer Earth, a few S heroes are on the ground; Tornado is doing her thing while getting irritated; a few C and B heroes are helping survivors. Genos, in the anime, is supervising Child Emperor. Saitama is the only hero on board the ship, where he wanders around trying doors and saying, "Hey, where's the head boss?"
He finds him and defeats him. The point is, he can't do that AND manage the stuff on the ground.
This assumption is so embedded that when Handsome Kamen Amai Mask shows up and castigates the heroes' failure to prevent all the devastation, the response isn't shame but disgust at his ego.
Genos and Saitama don't bother to argue (Saitama isn't there). One does the job one can. One does the job of the moment. A hero is a hero for coping, not for being all things to all people.
Saitama's consistent refusal to bargain his powers for special treatment
is part of this reality--and indicative of Saitma's inherent moral code, of which he seems largely unaware.
A great many things end up on his To-Do list because they occur in front of
him--or because Genos got himself into trouble. But the fact is, "It's in front of me" is the ultimate reality. Saitama only knows what he knows.
Genos and Saitama are limited and they expect to be limited.
It makes them, for all the monster-killing stuff, more relatable than many superheroes.
It likely helps that their reactions are delightfully pure young male.