Confusing, because the "pinchoff state" is the second one.  This state appears when the Vgs voltage is large enough that the channel becomes a constant-current source (because it's now being length-modulated by Vds voltage.  The channel-resistance is changing so as to keep Id constant.)  So, call it the FET "pinchoff-state voltage."

But the Vgs voltage required for cutoff state is entirely different.  It has little to do with the FET pinchoff-region.   Perhaps call it the "pinch-closed voltage."

As a kid I was very confused about these, and couldn't understand how FETs could even work, if the linear region only happens when the channel is entirely closed off.  DOH, "Pinchoff" is not pinch-closed.

Analogy: if you have a flow of water, then try to stop it by pushing two balloons in from the side.  It acts like a resistor.  Push the balloons close together, and suddenly they flatten!  Suddenly the width of the gap between the balloons becomes constant.  That's "pinchoff region."  It's a weird fluid-dynamics mode.  The water-flow in the gap between balloons starts acting like a slab of constant thickness.   The gap stops behaving as a resistor.  If you increase the water pressure, the gap region becomes wider, and the net flow stays the same.  Very weird, no?   That's Pinchoff operating mode.

But if you push the balloons together much harder, you can pinch-closed the water flow, reducing it to zero, and putting the FET into cutoff.