A Jump Ax Kick is a variety of an Ax Kick where one leaps into the kick (like a Jump Front Kick.
Similarly likewise with the Jump Front Kick, you hop with the very leg that you kick with.
The off-leg doesn't hop. All things considered, paving the way to the leap, you climb that knee up high to give your body some vertical force.
Then once in the air, you rapidly raise the kicking leg and afterward kick.
This is unique in relation to the Skip Ax Kick, in which the off-leg gives an exceptionally slight leap (i.e., a skip, or forward bounce).
https://elasticsteel.com/products/title-axe-kick-power-development