Few questions about BJT transistor

In a question regarding finding the Q point of a circuit and doing a general dc load line analysis i went through the following formulae
at Saturation Condition Ic(sat)=Vcc-Vce(sat)/Rc

i read another formula
Ic(sat)=Vcc/Rc

i understand the first formula (which is derived by applying KVL on the Outer loop) but i do not understand the second formula .. can someone explain this formula to me ..

at Saturation Condition Ic(sat)= (Vcc-Vce(sat))/Rc ≈ Vcc/Rc
Remember Vce (sat) is about 0.2 Volts so if Vcc >5
Vcc - Vce (sat) is nearly Vcc

The formula for Voltage gain of a common emitter amplifer operating in the active region with the emitter lead grounded is
|Av|=Rc/re , re is the internal transistor's resistance in the emitter, re ≈ 26 mV/ie for ie at 1 ma, re is 26 ohms. Remember in a common emitter the output signal is inverted with respect to the input signal
The formula for voltage gain of a common emitter amplifier operating in the active region with an emitter resistor Re that is not bypassed with a capacitor is
|Av| =Rc/(re+Re)

In the equation Icsat=Vcc/Rc they are neglecting the saturation voltage. This is reasonable if Vcc>>Vcesat.

The equations for Av are the AC voltage gain for a common emitter amplifier. The first one is for the case where the emitter resistor is zero. In the second equation there is an emitter resistor Re. re is a transistor parameter that is a function of the DC operating point and Hfe.

The "small re" value comes from very basic physics and statistical thermodynamics. If you imagine atomic scale particles moving around chaotically with various velocities then at any given temperature there will be some "most probable" velocity. If these particles are of varying masses, then you will get different "most probable" velocities for each varying mass. But the "most probable energy" of them will be the same, regardless of mass. Using Boltzmann's constant, k, and multiplying by the absolute temperature (usually in Kelvin), you get that value for the most probable impact energy. (Which impacts and drives an inserted thermometer, which then "reads" a "most probable" temperature as a result.)