If you search for square dance videos online, you will sometimes come across videos like this.
This activity seems to have many of the same figures and steps as square dancing, and this particular video also uses the words “square dance” in its title, but anyone who has been doing “normal” square dancing for a while will notice at least two big differences here. First of all, everybody is wearing tap dance shoes! Second, there is no caller. The dancers have memorized this routine. Other than that, there are eight dancers and they are doing movements like “square thru two” and “relay the deucey” and getting into squares and ocean waves.
This kind of dance is called “clogging” and it has developed in parallel with square dancing (and, in more recent years, line dancing). You can learn more about clogging here.