The Jump Button can be used in many ways.
By just pressing jump Lara will jump straight up.
If pressing jump and forward, Lara will jump forward. You can press left/right while in the air, to steer in this direction. This would be a standing jump. Lara can also do a running jump.
If you press left/right/back while pressing jump, Lara will make a side- or backsault.
In the water the jump button will be used for Diving.
Jumping forwards is slightly faster than the run , and a backwards jump covers slightly more area than a standing jump forwards.