Typically it is best described as Lead left steps into Follower Left, and then Lead Right steps into Follower Right. Sometimes you’ll hear this referred to as “Same Footed Walking” and that’s because that’s exactly what this is. The Lead’s LEFT is stepping into the Follower’s space where their LEFT foot was, so that’s the SAME foot.
There are 4 varieties of Cross System Walking that are described in the 6 Ways of Walking (as defined by Tango Topics). 1.) Cross System on THREE tracks, meaning that the partnership stays on three tracks where the center track is shared by both partners at the same time. 2.) Cross System on 4 tracks where the partnership walks together on same feet on 4 separate walking tracks in open or close embrace. 3.) Requires an orientation change where one partner is walking in front of the other. And 4.) Where the partnership engages in an orientation change and ends up walking on 4 tracks, but uses the Americana or “Sweetheart Embrace” to do it, only instead of walking in Parallel, you’re walking on the same feet.
It should be noted that sometimes this phrase is confused with the Argentine Cross. One has nothing to do with the other.