We can analyze the steps and basic movements of tango in many ways.
1) There are only two kinds of steps: cross and open. Always considered in relation to the partner.
2) There are three different steps: front cross, back cross and open/side. The follower's steps can go only to two directions: the leader's right or left. The leader's steps go either with or against the turn. (Yes, I know, especially the last sentence does not make any sense if you don't know what it means…).
3) My steps can go forward, back or sideways in relation to my own body, and they can be cross steps or open steps in relation to my partner.
4) The Mingo Pugliese system, based on the giro caminado (could not find the link, a great article!!!).
5) There is the walk, the ochos, and the giro. And then we add the extra elements like paradas, boleos, ganchos, sacadas, colgadas etc…
6) Linear movements and circular movements.
And these are just the systems that come to my mind right now! There are a million ways to analyze the tango dance, maybe even some that I don't know yet…
And all these systems want to explain the grammar of the body. The physical feeling of how the steps forward, backward and side connect to each other by rotation. How does it FEEL to make an ocho, and how does it feel to be led to a side step and into another ocho. How does the giro, the turn around the partner, connects to the walk.
I think this is the grammar of tango. You need to learn it with the mind and the body. And then you can play with it. Or you learn by playing...