Receiving is different than transmitting because there is no risk from SWR for starters. So your antenna match is far less important.

In many cases it is only an illusion that it is just a stick. An antenna on your car is using the car body and frame as one side of a dipole.

It is very complicated and few people really understand it. Take a look at this design. Part of the shield of coax is folded back over. Only the folded part of the shield acts like part of the dipole and only the extended center wire acts like antenna with the part inside the shield being feed line.

I made one and it is a great single band pack antenna that I can weave through the molle on my pack and it still beats a typical rubber duck on my HT. (A rubber duck on your HT is using you as the ground plane part of the antenna by the way)

https://www.hamuniverse.com/vertbazooka.html

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I was asking about receiving, not realizing it was any different than transmitting. I thought a poorly tuned antenna would give a poor SNR for receiving and not transmit as well when transmitting (though I don't know the metric for that).

When I said an FM antenna being a wire, I was thinking of a home stereo and an antenna like this:

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With those clarifications out of the way, the example was very helpful. I can't say I understand all the theory, but maybe I can take a crack at explaining what I think to be the case and we can iterate?

The waves come in and hit the antenna, inducing a current. In the middle section, it's blocked, but it gets in above and that's the resonant frequency, so the signal will be nice and strong. Below the double shield, the cable is still shielded, so it gets minimal interference on that segment.

I know my terminology is probably wrong here, but is that the gist of it?

Honestly, that FM radio antenna is a really crap antenna and you are thinking about a whole tier or 3 better design when you talk about a frequency matched dipole. I wouldn't be surprised if the length was unrelated to the frequency and just random. For receive only on signals as local and strong as FM radio it just doesn't matter much.

Yes, the way that verticle bazooka works is that the fold point changes the behavior of the wires in a way that causes it to act like a feed point on a dipole even though the core is continuous and the shield folds back on itself.

Antenna design is very much a case for the midwit meme with both ends being "just experiment and see how it works." Even people who are very knowledgeable are often surprised that a new design they encounter works at all.