At Challenge, we think of Crossover Circulate as "Circulate but do a Half Sashay as you go". At Advanced, there is more of a tendency to think of it as "Circulate but Ends become Centers and vice-versa".

I avoid calling Crossover Circulate when there's somebody in the #1 position of a Column. (for the #1 position in a Column, a Crossover Circulate is just a U-Turn Back. I wouldn't call it from here, as I think it may open a rat's nest of discussion)