Apparently the so-called "quadraphonic" format of vinyl LP's was before my time, but came and went like the Atari 5200. From what I get, it had more to do with the stereo speaker setup, with an individual track playing from each one, of four speakers. I'd found a quadraphonic LP of The Friends Of Distinction at a little thrift store next to the DMV and noticed on a regular turntable/two speakers, it plays an entirely different mix than the LP/single version (like the one from a CD release).
On the original version (of "Love Or Let Me Be Lonely"), everyone's vocals is soundboard-mixed evenly, not one singer overpowering another during the chorus. On the quad mix, Charlene's lead vocals (as well as the horn section) is front and center, and louder, with the vocals of Harry, Jessica and Floyd pushed back. I'm guessing what you hear on a standard turntable/two speaker plays as a different mix, and you're only hearing 1/2 of what you would if you played it on a quadraphonic setup. Maybe somebody a decade or more older than myself who's actually seen a quad can describe the whole thing to me someday because I don't really get it LOL!
Here's an example I made - the chorus to "Love Or Let Me Be Lonely", first as the original LP/single mix, followed by the same part of the song, as the quad mix I recorded from vinyl. Definitely a different mix between the two.
The full quadraphonic recording: