I assume you have examples where a dB isn't a dB, such as where the dB power gain is different from the dB voltage gain etc.
The point I was trying to make is that the 10log and 20log thing is simply an artifice to measure power ratios - you still get the same dBs. I think if you consult any authoritive reference you will find the bel is defined as log10 of a power ratio. It is then consistent to define it also as 2log10 of an amplitude ratio.
The bel is DEFINED as a power ratio? Okay, that's the type of thing I was looking for. So dB is always the power ratio for something or resulting power from whatever ratio of whatever amplitudes, and there is no such thing as dB to represent an amplitude ratio (though the dB can be converted with the 20log formula to produce the voltage ratio that would caues it). THen it makes sense to use 20log for amplitudes the resultant dB always represents a power.
But dBV? I've personally never seen a dBV. But the main thing I was concerned about is if you ran across a dB that was calculated using an amplitude, but you weren't sure whether the dB represented a power gain or an amplitude gain. If dB is always defined as a power gain, then you always know which formula to use (10log if you want to calculate the linear power gain, or 20log if you want to calculate the amplitude gain that produces that power gain).
EDIT: Okay, so it would seem dBV is using 1V as a reference, so I would think this technically means it is using the power in a 1V signal as the reference...with the actual power depending on the details of the system.
I suppose it also removes some confusion if dB is always a power ratio...you just say dB and the user can use whatever formula they want to convert that power ratio to a resultant linear power ratio or linear amplitude ratio. If there are power dB and amplitude dB floating around then if someone gets lazy and just writes dB rather than dB_there would be more confusion than there already is in practical matters.