A Heel Pull is much more closely related to a Heel Turn than you imply. But there isn't one 'correct' way to dance one.
Compare, if you will, the following:
Quickstep: Natural Turn with Hesitation
Foxtrot: Natural Turn
Waltz: Hesitation Change
Quickstep: Natural Turn at a Corner
Foxtrot: Impetus Turn
And see subtle variations in the width of the feet apart at the end (together, obviously, in the Impetus - the only actual heel turn). Note too the differences in the division (or not) of the Lady's turn. Much here for a student to ponder. But don't say in an exam that you draw the feet together - you don't. We are scribing an arc with the R heel around the floor, moving from one open position to another open position. By comparison, heel turns are a doddle.