In American numismatics the mullet is sometimes referred to as an American star, while the six-pointed version is described as an English star, but I've not been able to find any definitive source for such usage.
The so-called English star predominates on 18th and 19th Century United States coins, but it gave way to the American star for most 20th Century issues. Charles Barber's quarter dollar and half dollar of 1892 appear to have been transitional, as they feature six-pointed stars on the obverse and five-pointed ones on the reverse…
Monday, July 16, 2007
David W. Lange, an expert on American Numismatic wrote an article titled Seeing Stars were he sheds light about the usage of six-pointed stars on American coins: