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
I attended a seminar with then Olympic Coach Han Won Lee and he taught us to do the back kick without looking. He said in essence that the kick is linear and if you are fast enough, you are going to make contact with your opponent. The man could kick like a mule (and I am sure he still can.)
I can (at least intellectually) see that the no look kick could be a fraction of a second faster that the more traditional type since you are launching the kick without visually confirming the target is still there. It is still a dangerous kick to perform (both for the kicker and the intended target).
I've done both types and it is really difficult to "unlearn" something so I don't think I perform the "no look" kick as well as the original way I learned to perform the kick. I teach both types of kicks though.