What is the difference between step size and learning rate in machine learning?
Both learning rate $\eta$ and step size $\Delta w$ are linked to gradient descent. In the most simple case they are linked by : 

$$ \Delta w = w(t+1)-w(t) = -\eta \frac{\partial E(w)}{\partial w}$$

Where $t$ is the epoch and $E$ the error function.

In that simple case, they only differ by $ - \frac{\partial E(w)}{\partial w} $, which sometimes lead to use one term instead of the other. However in a more general case (learning rate depending on weights, learning rate depending on epoch, added momentum, or minibatch learning) the distinction may have a greater importance. 

Edit : I answered the title of your question, in the body you seems to refer to the number of step, which is the number of iteration or number of epoch of the aforementionned formula.