I think it's about time that some different names and different concepts should be formed and used.
There are two ways of perceiving pitch. One is by relating it to another pitch. For example, if I am in the context of a major scale, and someone plays degrees 1, 2, 3, I will know what 4 sounds like (a semitone above), and can sing it, or hunt around for the sound on an instrument. Or if I want F, and I have the sound of C, I can sing my way up the C major scale to get F. Or I may be able to hear intervals. If someone gives me the sound of Eb and I know that's what it is, I can go a whole tone higher to get that F. All this is relationional. It's like "the guy who mows the lawns", or "the guy who lives in the red house", but if he's not mowing lawns or near the red house, you don't recognize him.
The other is to recognize a pitch in its own right. It's wrong to associate this with names. You can recognize an apple for what it is, even if you have no word for apple. If I hear a single pitch, go to an instrument, and produce that exact pitch every time, then I am recognizing that pitch specifically. If I am singing a piece that is written in A major, the starting note being D, and every time I sing that song and check, I'm always starting on D, then I have a recognition of that specific pitch. It's not relational.
I think these are the two ways of perceiving pitch. Words like "perfect" get in the way. Tests of naming pitches eliminate anyone who can recognize them but has not learned names, giving a false negative.
I spent decades in a relative pitch world, and learned letter names very late in life. But I have experienced the second phenomenon which I'll call "pitch recognition" in both ways I described in my examples.