The BJT transistor is a current amplifier when the base emitter voltage is 0.6~0.7V like a diode drop. The collector-base is also a diode but is only lightly doped and reverse biased to function as a bas current controlled current amplifier. We use imepdance to convert current to voltage gain in the 1st stage and the second stage is need to amplify current to drive higher power (low resistive) loads.
The 1st stage we call "H biased" as it resembles the schematic, where the 2 input base reistor ratio sets the base then the emitter voltage is 0.65V lower and thus the emitter DC current can be predicted from hFE.
From from the collector /emitter ratio there is more drop on the collector so for the same current, there is now a voltage gain for DC as well as AC. BUT since the Emitter capacitor provides a much lower "impedance: This ratio for AC is much higher and is limited by the internal emitter reistance (not shown in schematic). We can estimate the voltage gain by looking at the specs and estimate the internal resistance for Re. This works well for small input signals less than 10% of the Vbe drop, since for AC the emitter cap does not allow much voltage swing. 100mV max is already distorted quite a bit. So we are converting voltage to current with impedance (V=I*R) and thus using the collector output amplifying voltage with impedance ratio and current gain of the transistor.
In the 2nd stage it is pure current gain and the ac voltage on the emitter matches the base as long as the Vbe stays at 0.6~0.7Vdc. Putting too much ( too low value) of a load like 8 ohms wont work on a 1Kohm emitter bias and will fail.
Why? Because the transistor actually controls the current by pullup to the supply. The resistor must pull down in order for the amplifier to be bi-directional for AC signals. With no emitter resistor to ground the emitter voltage would just float at the maximum AC voltage like a poitive peak detector.
Thus common speaker amplifiers use complementary pair output schemes with PNP and NPN devices.
This simulator allows to change any value and probe voltage, current & power.
Since the collector resistance is about the same as the input reistance, we say it is more a voltage amplfier, whereas the 2nd stage with emitter output is a current amplifier with < unity voltage gain. The ac load must not be < than the DC resistor.
Side comment: putting 2 complementary (in series) emitter followers ( NPN, PNP for + PNP then NPN for -ve) with large resistors and big capacitors makes a zero offset AC peak detector.