And yes, that's not the same as perfect pitch, which typically includes much more than the above. I certainly don't have it, even if I can pick any string first time in the morning and hear if it's "off". Because that's all I can do. But then again I don't get annoyed by "out of tune" sounds in the world around me, unlike what people with perfect pitch sometimes tell about.
I haven't seen anything equivalent for learning later in life though, although ear-training exercises clearly make your estimation better if you are disciplined about it, but that is relative, not absolute.
On bassoon I recognize all notes by their timbre. When I did this it started being something else. After a while I didnt recognize the notes. I just knew. I sometimes still have this. My harp colleague plays a note and I just know what it was.
I told this to a friend of mine who teaches solfege at college level (royal Danish conservatory) and she said that in her line of work perfect pitch isn't a gift it is a work-related injury.