That is correct. The flat part is "non-ohmic" meaning the current doesn't increase with increasing Vds difference. Of course, a resistor, which is ohmic, would show the expected change.in those Figs, after the curve turns almost flat line then with increasing in the Vds, why the current (Id) doesn't increase though? so Rds also increases with increasing the Vds? is that correct?
The significance of the non-ohmic region is that the mosfet junction is carrying all of the current it can at that particular gate voltage. It is "saturated." As you increase the gate voltage, more current is allowed until further increases in Vgs cause no further increases in current. At that point, the mosfet is "fully on." The maximum current when fully on often exceeds the current capacity of the device package.
When not fully on, more heat is produced as Vds increases and current doesn't increase. For that reason, mosfets doing PWM or any other switching, are usually operated fully on to reduce heating effects. However, in low power situations, you will see mosfets operated somewhat below fully on.