Current gain transforms to impedance between base and emitter by the current gain in each direction.
Thus CE has input impedance of β*Ze where Ze is the impedance on the emitter ( RLC)
and the output impedance looking at emitter is β*Zb , where Zb is the equivalent impedance applied to bias or filter into the base.
But since Ie≈Ic the impedance , there is no current gain but voltage gain is the impedance ratio of Rc/Re where Re is the source driving the emitter.
If the base impedance, bypass cap, β (or implied transimpedance, gm )and Ie all affect the low emitter input impedance so it usually sourced from a low impedance source like 50 Ohms.
A differential Amp has an equivalent circuit of a CE driving a CB so the output to increase Vgain, Add becomes -Rc/Re but has high input impedance.
In all cases the internal base-emitter resistance is assumed to be lower than
re but if not <<Re then it is included, which is normally in the < 10 Ohm range depending on bias current.
The only configuration that inverts voltage with respect to ground is Base to collector or CE .