Are the 2 singers in this track singing different notes?

Yes, that’s why I put “American” in quotes there. The Beatles are doing their version of an American accent–it isn’t perfect. And, of course, Galeazzo is another degree removed.

Here’s one, where the vocal solo is a single take at first, then doubled (at :36), then the same singer (Charlynn Maybe) switches to harmony with herself (at :44).

Incidentally, the same soloist was also 6 of the voices in the background in the chorus, where 4 voices (3 male, 1 female) were recorded 6 times, then mixed into a stereo spread (12 on each side).

The only example of non harmony singing I can think of is when the Glen Miller band shouts “Pennsylvania 6-500”, but that’s not really singing, is it?

Carmina Burana often has the entire choir singing in unison - sopranos, altos, tenors, basses, and all.

It’s also not uncommon for rock groups, at least, to have other members joining in unison for the chorus to thicken up the sound. I know in the bands I’ve played in, this was common, and in the concerts I’ve attended, this was fairly common, too. I’m trying to think of a recorded example–there’s got to be a bunch out there, but nothing is immediately coming to mind. Double-tracked vocals sung in unison have also been very popular since at least the 60s as a way of “thickening up” the sound. In this case, the lead singer sings the same vocal over him or herself (or sometimes this is done digitally or through tape tricks, like the Beatles did with automatic/artificial double tracking on much of Revolver and beyond.) Just Google or Youtube “double tracking” for examples.

Everything Bananarama sang was in unison.

I was briefly listening to music on the radio today (my radio is typically just set on NPR) and what I was describing as pretty common unison singing in the chorus showed up when Weezer’s “Beverly Hills” song came up. That chorus has unison singing. I’m sure if I kept listening, I could have come up with dozens more examples.

The Irish singer Enya took this to extreme measures, overdubbing both unison and harmony. The end result is like nothing I had ever heard before.