Does turning around count as moving for triggering Brace?

My fighter took Superior Technique as Fighting Style. This gives me the the Combat Maneuver Brace, from Unearthed Arcana, which says (emphasis mine):

When a creature you can see moves into the reach you have with the melee weapon you’re wielding, you can use your reaction to expend one superiority die and make one attack against the creature, using that weapon. If the attack hits, add the superiority die to the weapon’s damage roll.

The wording of a similar mechanic in the Polearm Master feat differs slightly:

While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter the reach you have with that weapon.

The word "enter" makes it very clear to me that the opponent needs to enter the reach for the trigger to happen, but "moving into" is less clear to me. It could be that they are semantically the same, but both my DM and I are unsure.

So, for example, if the opponent is already within my reach and it turns around to attack someone else: does turning around count as moving for triggering Brace?