To be sure, what you're hearing from that website is not coil whine (inductor phenomena), but mechanical resonance caused by piezoelectric effect on solid state MLCCs[1] charging/discharging in your monitor during frame refresh.
In common parlance, I'm not sure there's a distinction between coil whine and capacitor whine. That is probably not something you can distinguish without taking apart the component in question.
If by common parlance you mean amongst not electronics engineers, then I can see where you're coming from. The miscommunication that I'm seeing is asymptotic to the common misuse of Baud as a universal measure of bitrate...or in programmer speak, char and uint8 as immutable equivalents. From a hardware design perspective, qualifying the whine with coil transforms the remark from generally descriptive to technically specific with distinct implications.
Disassembly may not be required to trace root cause with high probability depending on the type of hardware exhibiting the issue, e.g. on a laptop, manifests upon affixing power adapter (as some have described) or tracks display pattern (as parent link).
[1] https://en.wikipedia.org/wiki/Ceramic_capacitor#Microphony