Mass and Weight are Different.
In zero gravity a punching bag is weightless. Still, you cannot punch it into the ceiling with a fingertip. This is because the bag is too massive. Mass is a body's ability to resist movement and doesn't change with gravity.
In ZG if you prod the bag with your fingertip millions of times it will reach the ceiling. This is because the bag stays in place between pokes. This won't work in gravity because the bag resets after each poke.
In ZG if you poke the bag enough it will eventually hit the ceiling. That's because each poke gives the bag a sliiiiiight momentum that is not cancelled by gravity. So poke the bag one and wait a year for it to hit the ceiling. Or poke it a few million times and watch it fly!
Now replace the punching bag with a Martian on Mars. You won't send them flying unless they are stick-thin and have little mass.
Likewise, your jump speed will not increase on Mars. What changes is the max height of the jump? It might still take a while to reach the top of that skyscraper.
Probably your top speed is lower on Mars. Your legs have the same mass so each stride uses the same energy. So you could make the same number of strides per minute. Only now with lower gravity each stride pushes you higher into the air so you take longer to land. So fewer strides and less speed.
Your heart can pump the blood from your feet to your head more easily. This might change endurance. I'm not sure exactly. It might cause other problems too, like unnaturally high blood pressure
You're not stronger -- they're weaker.
The usual story is that evolving in low gravity, the Martians did indeed evolve to be much less massive. For example, they can get away with lighter, weaker bones, and less muscle.
Let's say Martians weigh about 30kg. About are half the mass of a grown human. Depending on their biology, your fist might go straight through a Martian's chest, or you might stagger them a few feet. This probably depends on where you hit them. Hit near the top bit of the Martian they will move back further as they try to catch themselves.
From a scientific point of view, I find a huge difference in strength hard to believe. The skeleton is only 15%ish percent of the body weight. Perhaps a smaller heart to pump blood up to the head, but most of the body is not there to resist gravity. Remember there are other stresses. Such as the stresses caused by the body on itself when turning suddenly.