# difference between max() and max^(0,1)

I have a really complicated function that I need to take partial derivative of. After executing the partial derivative, I got a function that contains both $$\max(0,a-b)$$ and $$\max^{(0,1)}(0,a-b)$$ for some constant $$a,b$$.

I know what $$\max()$$ function does but I've never seen $$\max^{(0,1)}$$ before.

What is the difference between those two functions? Is $$\max^{(0,1)}$$ simply outputting binary (True/False) result?