"You may not wan't to call it a THT but you better use the ball toe of the RF if you want to push off from it into the next slow,so I dont know what else you would call it "

It's still unclear what step you are talking about, but rest assured there is no step for either partner in the feather which is danced "THT".

The core problem here is that you are using a precise language casually. Review Moore's definitions on footwork terminology and you'll understand that when a part of the foot is specifically mentioned in the letter code it must be reached before the end of the step, however the usage of other parts of the foot after the end of the step is in some cases implied, but will not be part of the letter code because it is not part of that actual step but a follow through action instead.

The way the body leaves a TH step to move forward to a H or HT step, is different than the way the body leaves a HT step to move to a T step.

Formally, the means of departing the TH step 3 of a feather towards step 4, is the same as the means of departing the H step 4 of a feather towards step 1 of an (ISTD) three step, in that the toe of the standing foot is reached only after the new moving foot has passed to end the step. In contrast, the HT step 1 has the weight reach the toe before the end of the step.