Short answer. Pole heels is dancing and holding on a pole, in platform heels. Heels dance is dancing in those shoes with no pole. Booking the wrong one is an easy mistake because both say “heels”.
Pole heels
The pole is in the phrase because it is in the class. You use it. Flow Factory lists pole heels as its own track, with initiation, level 1 and level 2, and a women-only Pole Heels Intro on Saturday. Skin still meets the pole, so shorts still matter. The shoes are added, not substituted for grip.
Heels dance
Heels dance, sometimes just called heels, is floorwork, walks, turns and choreography in platform shoes. Flow Factory describes it as technique, confidence and style, from walks to choreography, and marks it open to all levels. There is no pole in that description. Grip products are irrelevant. Shoe comfort is the whole problem.
Air Dance School’s Flagey page lists “pole heels”, not a separate heels-without-pole class, on the line checked for this guide. Do not assume every school splits the two. Read the class title. “Heels” alone, on Flow Factory’s timetable, is the class without the pole. “Pole heels” is the other one.
Which to take first
If the pole is the reason you came, take pole, barefoot or in socks, before you add shoes. If the shoes are the reason, a heels dance introduction is the direct class. Taking both later is common. They train different balances.
Shoe choice for either path is in choosing your first shoes.