He gave us a very simple explaination that:
Standard deviation: asymptotically, this estimate will be sigma.
Standard error: asymptotically, this estimate will go to zero (as n is in the denominator of the formula, and as it goes to infinity, SE goes to 0).
This seems to be an obvious answer once we look at the formulas of the two estimates. Nonetheless, Andy said that he sometimes uses them interchangeably.