They are similar, but are each applied depending on the context. Stand back implies you are close to a situation and need to move slightly away. Stay back implies you are already there/back, and are being encouraged to remain there. Step back is similar to stand back, but perhaps implies a smaller distance (hence the step). Just my thoughts :)

It is easier to answer with a context. Suppose I am playing with a sword and you are in front of me. If you "stay back" it means you do not want to get closer but stay where you are, at a safe distance If you "stand back" it means you are standing, and at a safe distance. It includes the idea that you may have to move to where it is safe If you "step back" it means that you are moving away - step is always an action. You walk back while looking at me