Those are the Italian fouettees
I am assuming the Italian school (Cecchetti school) started using Italian fouettes as regular fouettes, so then the other countries started labeling them Italian fouettes. Or does someone have another theory or know the answer to California's question?
I assume it was probably where the step was first developed. Fact is,the two steps differ from each other in both design and pace, starting with their different time signatures-(regular fouettes in 4/4 vs. Italian fouettes in 3/4)