Pinch-off voltage is the voltage across the drain to the source of a FET, after which the drain to source current becomes constant or the FET goes into saturation region and it is defined when the gate to source voltage is zero. So we can say Pinch Off voltage is the value of VDS or drain to source voltage at which the drain current ID gets a constant saturation value.

In the below figure, you can see the pinch-off region.

So, you can understand the pinch-off voltage is not a particular voltage. It is a range of voltage. Although the meaning of Pinch off is threshold so at the voltage from when the current gets constant is referred to as Pinch Off Voltage. It can be understood very easily with an example.

For example, the VGS or gate-to-source voltage is zero. Now, at starting 2V is applied across the drain to the source(VDS) and it is increasing rapidly. Let's assume that the starting current flow was 1A and it also increased as the VDS increased. Now when the VDS reaches 10V, the current flow reaches 5A. Now, up to 15V current flow constant at 5A. After 15V the FET got to break down or it goes avalanche region and a very high current starts flowing. The voltage between 10 to 15V is called pinch-off region voltage. It may be any voltage such as 11V or 12V or 12.1V.

The pinch-off region is mostly seen in the JFET or Junction Field Effect Transistor. Also, you will see the pinch-off region in FET is very similar to the linear operating region of the Bipolar Junction Transistor or BJT.

Now, let's understand actually what happens in the pinch-off region. In normal conditions, when the gate-to-source voltage(VGS) gets more and more negative the channel of the JFET becomes narrower. But in the case of the pinch-off region when the drain to source voltage is increasing the conductive channel also grows physically longer. So the internal resistance property tries to make the current flow constant even when the voltage is increasing.

Pinch Off region happens in JFET(Junction Field Effect Transistor), and IGFET(Insulated Gate Field Effect Transistor). For a JFET transistor, Pinch Off referees a threshold voltage below which the transistor gets turned off. On the other hand, for an IGFET Transistor, The Pinch Off Voltage refers to a voltage at which channel pinching happens and the current flow gets saturated.

So don't confuse with different types of voltage such as,

1. VDS - Voltage across Drain to Source

2. VGS - Voltage Across Gate to Source

3. Pinch Off - Voltage across the drain to source when Drain Current constant and VGS = 0