I know I've recently lost the perfect pitch I was born with and had virtually all my life.   If my mother would play be notes or chords on the piano, I'd always be able to state each note....very quickly.   Occasionally, if it were more than 3 notes in the chord she might have to play one right after the other. (Yes, of course I had to be taught the 'name' of the notes first).

Recently, since I 'lost' my perfect pitch (which has been documented as happening to some people with age) I took one of those online perfect pitch tests....and it told me I had perfect pitch.   But I know I don't....it's not the same. I had to work at it and sometimes I got it wrong.   

So this is an example (as per the heading of this thread) where what is classified as 'perfect pitch' really isn't.

So it may be that there aren't 'levels' of perfect pitch.....we either have it or we don't.