Flatfooting is a close relative to Mountain Style Clogging, (in fact it's a precursor) but uses only softer versions of the shuffle and buck. Very few people still Flatfoot, but it is not uncommon to see an elderly gentleman or two Flatfooting at Appalachian music festivals. Shoes have no taps, and clothing is generally whatever you've got on when the mood strikes.
Buck dancing is more like Clogging than Flatfooting, and is easily confused with it. However, due to the fact that this dance is also older than clogging, the steps, are still less complicated. Shoes usually sport taps.
Square-Dancing can be easily integrated with Clogging, but is actually a dance of stage location rather than dance steps. Some Square-Dancers Clog when dancing, and sometimes traditional Cloggers use Square-Dance patterns in their choreography. Shoes can have taps or be tapless.
Tap is, of course, the most popular dance in America. Its steps are executed much faster than Clogging, however, and dancers place most of their weight on the toes. Cloggers emphasize both the toe and heel positions. I once had a friend who, when trying to show me a Tap step, comment on how I danced "just like a clogger" because I kept stomping my heel instead of my toe! Shoes have single taps at toe and heel, an occasionally have a form of double tap at toe. (See diagrams.)