https://www.universityofcalifornia.edu/news/singing-memory-u...
It's the being able to name a note and sing it or hear a note and give the name that's rare.
Few people do this because it's simply not practical, but that 44% of recordings match the pitch of their source exactly shows pretty conclusively that there's nothing magical behind absolute pitch, it's just that most of us learn to associate pitches with songs rather than giving them names.
There is something special about musical memory. When I was starting out as an anime fanatic I would quickly learn to sing theme songs like [1] [2] although I didn't understand Japanese at all then.
Notably different language have different words for colors, for instance the Japanese word 青い (pronounced aoi) can mean either blue or green. [3] There's been a lot of controversy over whether language shapes perception, but if you do psychophysical tests that don't involve language you find people can tell colors apart pretty much the same no matter how rich or impoverished their vocabulary is [4].
[1] https://www.youtube.com/watch?v=2hulET9tn9M
[2] https://www.youtube.com/watch?v=XW9BapLxwkw
[3] ラム (Lum), the girl with oni horns and a tiger stripe bikini who appears in [1] has 青い-colored hair which seems to drift in the blue-green area throughout the 5-season anime
[4] https://en.wikipedia.org/wiki/Linguistic_relativity_and_the_...