basic b\w of cut off voltage and potential deffrence?

In short, threshold voltage(cut off voltage) is a specific form of a potential barrier. Let`s say point a is at a potential Va and point b is is at a potential Vb, where Vb>Va. Then the potential barrier between them is Vb - Va.Threshold voltage is more specifically used in case of a diode or a transistor. The gate bias (in case of a MOSFET) or forward bias (in case of a PN junction diode) required to overcome a certain potential barrier to turn ON the device.However, in the recent short channel devices, tunneling can occur before you reach the threshold voltage. That`s altogether a different issue, though.