"Hax jump" is some glitch in the engine which allows you to jump vertically a lot higher than you otherwise could, without needing edges and such. I think it has something to do with glitching into the ground slightly, and jumping while the game pushes you out of the ground, or maybe multple jump commands in the same frame. I don't actually know how the engine mechanics of it work, this is all conjecture, but the point is that it is most certainly a bug somewhere.
"Crouch jump" usually refers to crouching while in the air, after jumping. This brings your feet up higher letting you get up to higher ledges
"Edge jump" refers to using edges to jump higher / farther. If you time it right, you can jump off the ground, and then off a slightly higher cube edge (or mapmodel or clip) to increase your vertical and horizontal speeds. It is the same effect or related to how when you run up stairs, you can spam the jump button to run up the stairs a lot faster
I don't actually know what people mean by "Double jump". I've never seen nor heard of anyone doing a double jump in terms of what that means to other games (jumping, and then jumping again mid-air, without anything to jump off of), so clearly the term is misleading.
"Crouch jump" usually refers to crouching while in the air, after jumping. This brings your feet up higher letting you get up to higher ledges
"Edge jump" refers to using edges to jump higher / farther. If you time it right, you can jump off the ground, and then off a slightly higher cube edge (or mapmodel or clip) to increase your vertical and horizontal speeds. It is the same effect or related to how when you run up stairs, you can spam the jump button to run up the stairs a lot faster
I don't actually know what people mean by "Double jump". I've never seen nor heard of anyone doing a double jump in terms of what that means to other games (jumping, and then jumping again mid-air, without anything to jump off of), so clearly the term is misleading.