Foot patterns do not a dance make.

Tango is Tango because of the quality of movement; The dramatic, staccato actions, the lack of swing & body flight, the dance position, and even the facial expressions. These are the things that work together to characterize the dance. It hardly matters what foot goes in what direction.

Arthur Murray made a fortune on the concept of the "inter-related system", showing that a simple box step can be characterized in many different ways. Depending on how you dance it, you can have a Waltz, Foxtrot, Rumba or even a Samba. The same goes for the Cross Turn you mentioned, which has been seen in some form in almost every dance, Standard or Latin, American or International style. It's even considered a fundamental syllabus figure in Viennese Waltz, Tango and (yes!) Samba, and has been for years. Many American style syllabi also have it in Waltz and Foxtrot.

The moral of the story: Concentrate less on what step you're doing, and more on how you're doing it, and you will eventually start to make sense of the key elements that characterize a dance.

Regards,
Jonathan Atkinson