Is activating a phone on "T-Mobile" paying full price considered unlocked since I paid full price on it?

On best buy, per se, there is a promotion going on that if I buy a phone though a T-Mobile specific deal and activate the same day I will be paying ~10% less as opposed to an "Unlocked" phone and activate it on the same day through my carrier plan. My questions are below:

1. Since I will be paying the full price after the deal, is it going to be unlocked?
2. If not, why? And, when will that be eligible for unlocking?