If you assume that r8c5 is 2 and follow along what that implies for the rest of the puzzle you come to a contradiction fairly quickly. So r8c5 does need to be 5. However that is a fairly complex technique. All that is required to solve the last puzzle is naked pairs, locked candidates, and singles, so it is difficult to see them resorting to Nishio (follow the implications of assuming a cell contains a specific digit and check for contradictions along the way).
Based only on the first example, it seems like Digit Rule is what we call Naked Single, only one digit is valid in the cell (all others are directly contradicted by already placed digits).
The second example is a little more complex, as there is a very simple move readily apparent. By Full House r2c3 must be 1. If that isn't mentioned it makes little sense to talk about r8c5. If r2c3 wasn't mentioned, perhaps there are several steps missing before you get to r8c5. In several simple steps you could easily get to a situation where r8c5 becomes a Naked Single.