So basically it's called lumped because we treat all the elements as having the properties of ideal elements without discerning between the individual elements themselves? I guess that makes sense, it just seems like a strange use of the word. I guess something like "ideal circuit elements" would make more sense to me at least. Any idea where the use of lumped in this case came from?

Thanks, that makes sense because the filter caps are aluminum electrolytic which according to the Wikipedia article have the highest rate of dielectric absorption.

Thanks for your answer. So is it fair to say that sometimes the two formulas equivalent and sometimes they are used in different scenarios and aren't equivalent?

I read that question and all the answers prior to asking my question. I don't think this is a duplicate because nobody mentions the impedance or the disappearance of its terms in the formula.

Thanks @olin, this helps explain it. I can take it on faith for now but still have a related question. If I take for example a non-inverting op-amp circuit and set the voltage gain using the feedback voltage divider, do the impedances still not make a difference in the decibel calculation? Because if I understand correctly, the input impedance would be much greater than the output impedance.