When you have perfect pitch then your brain acts like a frequency counter. You hear a tone and you know what pitch (frequency) it has. You can tune an instrument without using a reference tone to beat against.
Some people are not musical and do not recognize musical chords and octaves. To them, music is simply a bunch of sounds (noises?).
I can hear that a musical tone is slightly out of tune. It sounds "wrong". Singers make recordings many times over and over before everything is perfect (24 takes?) but when they sing on a live show I can hear the mistakes they make when they are slightly out of tune and sound like amateurs.