I have tried to look at how these, gain and dB's, relate to one another, but there seems to be nothing solid on the Internet. Perhaps I am looking in the wrong places.
The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity. One of these values is often a standard reference value, in which case the decibel is used to express the level of the other value relative to this reference.
In electronics, gain is a measure of the ability of a two port circuit (often an amplifier) to increase the power or amplitude of a signal from the input to the output port by adding energy converted from some power supply to the signal. It is usually defined as the mean ratio of the signal amplitude or power at the output port to the amplitude or power at the input port. It is often expressed using the logarithmic decibel (dB) units ("dB gain").A gain greater than one (zero dB), that is amplification, is the defining property of an active component or circuit, while a passive circuit will have a gain of less than one.
The term gain alone is ambiguous, and can refer to the ratio of output to input voltage (voltage gain), current (current gain) or electric power (power gain).
But even simpler, dB is just a relative shorthand that is often used to describe gain. Nothing more. It is often used instead of the linear value because it leads to smaller numbers (instead of dealing with numbers like 1000 or 1 million you have 60 dB or 120 dB) and it makes certain mathematical operations simpler to do in your head.
but there seems to be nothing solid on the Internet.