Current in Saturation and Active regions of BJT
Perhaps it helps to give some explanation to the term "saturation".
Yes - there are two different meanings of the term "saturation" - dependent on the transistor type: BJT or FET. In this context, we should answer the question: Where is this term coming from - that means: Which quantity is "saturated?

1.) BJT (with collector resistor): Increasing Vbe (or Ib) leads to rising collector current Ic, which causes a continuous decrease of the collector-emitter voltage Vce - until a lower limit is reached at app. (0.4...0.6)volts. A further increase in input voltage/current does not cause a further increase of Ic. Thus, Vce has reached it´s lower limit and cannot become smaller. We say: The voltage Vce has reached the state of "saturation"(and - at the same - time the current Ic cannot assume larger values).  

2.) In contrast to this effect, for FET´s the term "saturation" means something else. For small drain-source voltages Vds we have approximately a linear relationship between Vce and the current Id (for a fixed control voltage Vgs). This region is called "linear region" or "resistor region". However, for further increasing the voltage Vds beyond a certain threshold (pinch-off) the current Id does not increase anymore (in fact, a slight increase due to channel width modulation can be observed). That means: The  current Id has reached the state of "saturation".

Summary: It is an unfortunate situation that two different meanings of the term "saturation" are in use (for BJTs and for FETs), but - due to historical reasons - we have to be aware of these two different definitions.