CMOS basic question: saturated transistor

I have a pretty basic question about CMOS devices. Let's say beside the well known equation what is the real meaning of the saturation condition ??
I know that the channel gets pinched but where it comes the condition from?( that Vds>Vgs-Vth).
I pretty much know all what that happens there and want to understand intuitively...
Like I really see what it happens in a bipolar transistor that gets saturated when the collector current cannot follow the β*Ib rule due to the limited collector potential.

Coming back to the mosfet saturation condition... Is that just mathematically deducted ? How do you guys see that and if we are to take an example from let's say fluids and pipes...can you light up the bulb for me ?
I hope I'm not bothering,
Thanks a lot

Because Vds = Vgs - Vgd, if Vds > Vgs - Vth, then Vgd < Vth. So Vgd can not control the drain current, the drain current is only controlled by Vgs.

Thank you