On a controller that has thumbsticks, when it is possible to press down into the thumbstick - not D-pad down, as in UP/DOWN/LEFT/RIGHT, but down on the Z-axis - what verbiage would one use to describe this?

Pictured above: Blue arrows indicate d-pad directions, and a green arrow indicates the inward down direction.
Saying "press down" could easily cause confusion with d-pad directional "down".
There must be some language used in the gaming world to express this.