Is the meaning of a Decibel different when applied to Voltage vs Watts?
Deci-Bels always express a power ratio.  Specifically, dB is defined as 10Log10(pwr2/pwr1).  Therefore "20 dB" is exactly the same thing as "100 times as much power".  This power ratio is never ambiguous, but sometimes what it applies to can be.  However, this is no different than for a statement like "100 times as much power".  It may be ambiguous what has 100 times more power than what else, but the ratio itself is clear.

dB are sometimes used to specify gains of amplifiers that work on voltages.  Since dB always specifies a power ratio, and power is proportional to the square of the voltage, dB in this context can be thought of as 10Log10((V2/V1)&sup2;), which is the same thing as 20Log10(V2/V1).

Power depends not only on the voltage but also the impedance that voltage is driving.  Sometimes those impedances aren't know, or the system works inherently with voltages and the actual power isn't relevant, so the simplification is made that the power ratio is the square of the voltage ratio.  This is often the case in audio circuits.  In other applications, like RF, the impedances are known and important, so then they are taken into account and dB represents the actual power ratio.