The terms syncopation and syncopated step in dancing are used for two senses: Many dance teachers criticise the use of the term "syncopation" and abandon it in favour of the term "double-time".
That is most likely because of a convenience in similarity and/or a misunderstanding of the rhythmic concept.
Dance syncopation often matches musical syncopation, such as when (in West Coast Swing) the leader touches slightly before beat 3 or stomps on beat 6.