What's the actual difference between voltage gain, current gain and power gain?
Gain is simply output/input, for example Vout/Vin. So for an emitter follower you cannot say that "it has no gain" because it does!

An emitter follower has a voltage gain, Vout/Vin of slightly less than 1. (and this is what you mean by "it has no gain", indeed the signal voltage isn't increased).

But an emitter follower can have a current gain Iout/Iin of much more, use the right transistor and the current gain can be a factor 500.

To achieve power gain Pout/Pin we must realize that Power = Voltage x Current so if we change the Voltage and/or Current such that output power is increased, we have power gain. In the case of the emitter follower, most power gain is due to the current gain.

For a common emitter circuit, both voltage and current gain can contribute to power gain of more than one.