Nowadays I imagine only a small proportion of people who deploy "radio buttons" have even seen such a car radio, so the metaphor is now empty, like the floppy disk icon for "save".
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Basically a "radio button" interface is a mechanical XOR. So for example to route a signal to destination A, B, or C you'd want to push the A button and be sure B and C weren't selected. Often it mechanically latched, so you could also see at a glance which option was selected, rather than needing to have an indicator (typically a small incandescent bulb).
Radios themselves implemented that mechanism slightly differently. Each button had a stop (like a tab stop, not an organ stop). When you pushed the button it disabled all the other stops and then either a spring pulled the arm right to the stop or your own muscle power pulled it left. A pully rotated the tuner dial as the arm moved right or left. I believe the buttons were rectangular in order to have enough surface area for your finger to supply a firm press enough to pull the tuner arm all the way from right to left (the extrama case). If they'd been round they would have taken up too much vertical space.
The radios typically had five or six favorites, no more. The entire mechanism was mechanical.
I did have a tape player with buttons (play / rewind / stop / etc) that, when pushed, unpushed the other buttons. So I have a mental model for buttons of that kind. But I've never associated them with a radio.
Also, I've never associated the radio selector HTML element with a button (HTML or otherwise). Buttons are about triggering effects. But radio selectors are about selecting something; they have more in common with checkboxes.