The to kicks described here are as I know, 1. spin back kick 2. spin side kick.
The back kick striking surface should be the bottom of the heel. My sabo had often referred to this kick as a 'horse' kick or 'mule' kick, because it is done in the same fashion. Students are taught to execute this kick with their back facing the opponent, while glancing 'over' the shoulder to confirm the target. After years of experience, we learned to throw the kick without looking. You basically point the backside of your knee towards the target, and execute the kick the same way. It lands square, just the same. Your instructor was probably trying to get you to distinguish between the two.
the second kick is more or less executed in 2 parts, from what I've been taught. First would be the spin with the chambering of the leg... and then secondly the kick. Often used for deception, because from that spin you can go into any single legged attack... so this technique is less committed than the first. Just my .02