Whatever you call it (some of the other terms come from square dances of particular names, such as Old Mill Wheel or the Wagonwheel Star), today a wrist star is the US standard for most of the country.
That said, the square dance movement uses a palm-in star (which I personally prefer for most applications and find prettier). That was the standard style around Colorado in the 1930s when Lloyd Shaw got started, and for many years after. Pretty much, you'll only find it among square dancers, people who danced with Calico and Boots in Boulder, Colorado, or folks with an exaggerated respect for history. Guess I qualify as all three.