Confused about the definition of voltage gain
dB is never voltage or current gain. It is always power gain. Your equations that find dB using voltage or current are not finding voltage or current gain. They are finding power gain using voltage or current.
If I say something increased by 10dB, I am saying it increased by 10dB in power. Not voltage, current, nor any other amplitude. You can determine how much an amplitude increased from the 10dB increase in power, but the 10dB itself is always talking about the power increase.
I don't know why it was defined this way, but it is.