I read that in transfer characteristics of JFET, Vds is kept constant and Vgs is varied. But when Vp for any device is constant and Vds is also constant then even Vgs should be constant.
To the left is the transfer characteristic plotting Id against Vgs and to the right is the graph that shows the various conduction regions of the device.
The left hand plot is derived from the right hand plot by taking the points when Vds is at 10V (usually but not always) and translating across to the left hand graph so you get a plot of Id against Vgs.
Pinch off is where the device cross from being ohmic to saturating : -
Maybe you are confusing this voltage with Vgs(off)?