They don't call 'em
Jump and Shoot man for nuthin'.
It would be accurate to say that Super Mario and Mega Man use jumping very differently though. Super Mario typically designs all of its mechanics around jumping, so it's your attack, it helps you land fire balls, power ups often amplify it, etc. However, while you have to make full use of your jumps to take out/avoid threats and such, the jumps themselves are rather tame. Mega Man is the opposite; you have to shoot to beat enemies, and none of the weapons that you get interact with the jump in an organic way (even the utilities are special platforms rather than additions to the jump ability). Even so, Mega Man games throw the most b.s. jumping puzzles you'll ever see:
View attachment 324541
image from the Mega Man Home Page
Here, you're supposed to run back and forth on this swing to allow you to get close enough to jump to the ledge, but not jump so far as to kill yourself on the instant death spikes. This dosn't even make the top 10 list of worst jumps in the series.