The result seems to me to be more like Reverb in my perception/use.

You’re on to something: reverbs often intentionally create resonances. Reverbs can be simulated with a filter (although commercial reverb plugins and hardware typically sprinkle in some non-linear goodness).

What does the absence and abundance of resonance reify as observably?

In audio systems, it sounds like you added ringing to the signal. If it’s too much ringing, eventually the ringing will dominate over your signal and you’ll basically get a sine wave at the resonant frequency.

Below is a response of a filter with a resonance:

You’d have to show me a diagram or plugin with the control labeled “R” to be sure, but I believe that with respect to the above diagram, R is equivalent to ζ (zeta). However, some plugins use Q = 1/(2ζ) as the parameter for the user to change, in which case the intuition is practically “backwards”.

When ζ is about 1, the system described by the graph basically doesn’t ring. As ζ goes to 0, the resonant frequency and its neighbors start to get boosted, giving the characteristic “ringing” sound. If ζ = 0 (or practically is close enough), you get an oscillator, i.e. you generate a sine wave with the resonant frequency.

What does R refer to or what is it a spectrum from->to?

The spectrum of the filter is actually the curve above, along with its phase curve, which gives you the output of the resonant filter given any input. ζ and Q are different ways of specifying the strength of the resonance.

Note that I used a filter with just a resonance for simplicity, but any filter can have a resonance, including low-pass filters, in which case ζ is often used as a parameter in the math. You can logically think of a resonant low pass filter as a “non-resonant” low pass in cascade with a resonant peak (order doesn’t matter) at the same frequency you set the low pass to, even though they’re not designed that way.