They are actually both correct.

The more natural definition is the voltage that cuts off the changel and reduces the drain current to an extremely low level.

However the pinch off voltage also sets the voltage at which the device transitions from the linear region to the saturation region. As the drain voltage increases it tends to close off the channel and cause the current to remain constant rather than increasing linearly as in the triode region.


[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/7rB4H.gif