In Super Metroid, is jumping after running not just as fast as running on the ground?

Solution 1:

No, running on the ground is faster because of a tech called Arm Pumping or Shoulder Pumping. While you are running, if you move Samus's arm cannon up and down it advances her forward by 1 pixel.

This is much faster than jumping and can be controlled anytime while Samus is on the ground or not in ball form.

Jumping in Super Metroid isn't entirely too difficult, but it's not about wanting to spend more time on the ground. It's about wanting to advance Samus forward as much as possible.

Here's a link to a video showcasing it

More info via OmnipotentEntity: Shoulder Pumping does not change the speed of Samus in memory, every time you pump you move Samus one pixel forward. Jumping conserves your speed when you leave the ground, but when you land your speed is reset to 0 (unless you land as a ball.) You can find more info about Samus's movement on the TASVideos page on Super Metroid: Here