I think what you're talking about is known as a kip-up in gymnastic terminology. This is where you are on your back and want to spring
back on your feet in the quickest time possible. This can be done with hands, by the sides of your ears, or without using more force with legs and hips and requires more flexibility.
A front hand-spring is a hand-stand then going over forward and springing to your feet, all in one quick motion. A back-ward hand-spring is like a back flip, but landing on your hands first, then allowing the tension of the arch made by your back to propel your legs up then over your head in the opposite direction, kind of like a back-walkover but with a leap followed by a quick whip-like motion of your feet over your head.
Depends on your age,flexibility and no-fear factor these can be learned and perfected quickly. Having a gymnasium with a coach and waist/hip harness for spotting will be a big help, not to mention protecting your head and wrists during the learning stages.
I learned all 3 when I was 15 y/o. It get's harder after 25.
A back hand spring with no hand and only legs is a back flip. I can do a front hand sprin WITH hands, and a no handed kip up. Few other tricks like that.