Regarding symbols used for current amplification factor
The alpha, beta and gamma are not actually representing the same thing.


In a common emitter, you input base current and take the output somehow related to collector current. So, Ic/Ib = beta becomes your current amplification ratio for common emitter.
For a common base, you input to emitter and take output from collector. The emitter and collector currents are nearly equal. So the amplification ratio is alpha, which is a value very close to 1 but less than 1.
In common collector configuration, you input the base current and
get the output from emitter, so the ratio is Ie/Ib which is
gamma, slightly higher than beta.




Ie = Ib + Ic
Ic = beta * Ib // common emitter 
Ie = gamma(beta+1) * Ib // common collector
Ic = alpha * Ie // common base


You may find this video helpful.