Perfect pitch means you can hear a tone or multiple tones and identify them. There was a girl in undergrad music theory class at UK who had perfect pitch. She described it as painful if a vocal ensemble was to lose pitch, i.e. go flat/sharp.
Another person I worked with professionally was a local band director wife. We could use her as a tuner, because she not only knew the pitch, but whether you were ever so slightly off. We would bring her in periodically to critique and the students always enjoyed trying to “trip her up”. But perfect means perfect and they never could.
In one rehearsal, without a score in front of her, she made a comment like, “The Bb7 chord at letter E is both wrong and out of tune. The altos have the ‘D’ (your ‘B’) and one of you is playing a Bb and another of you is playing the right note, but quite sharply.” We checked. She was perfect.
I do not have perfect pitch, but good “relative” pitch. It serves me well in two general ways. First, as a clarinetist, I can usually “hear” the pitch before I play it and so can come in on the right note/partial and on pitch. Especially when listening to a clarinet, I can usually tell you the note, but more because I know the different timbres of notes. An open ‘G’ sounds different than a ‘Bb’, for example.
It also serves me well in rehearsals as I have keen “hearing eyes”. I can tell if what I’m hearing is what I’m looking at in the music score. I established that when I would say, “Someone is missing [specific note]. If you don’t fix it, I will find you”, they knew I could, so sometimes, when I stop the music, look down at the score (to figure out what I heard and where it might be coming from) and focus my attention toward a section of the group I might find someone with his/her hand already raised to confess, “It was me”.
During a grad class, I had to stay after class one day because I was doing something the professor said I shouldn’t have been able to do and he wanted to find out how I was “cheating”.
His researched position was that you could only retain and re-sound about 8-11 random tones. To make his point, he emphasized why phone numbers are broken down; 260-786-6554 vs 2607866554 or that credit card numbers are “batched” in 4’s because we can’t remember 16.
Then for practical proof, he started playing series of tones. We were to sing them back and drop out when we missed. Not unlike a spelling bee, by the time he got to 12-13 tones, there were only two of us left. The other person dropped out and the professor, in a frustrated tone, asked me how I was “cheating”.
Working 1-1 after class, he noticed (I didn’t even know I was doing it) I was fingering my pencil. His conclusion, and I had none better to offer, was that I was “hearing tones in clarinet” and then “playing them back”.
What I did was not unique. I know of others who have trained their ears to hear specific pitches, such as an ‘open G’ on trumpet or a vocal “do” on ‘c’.