blitz vs classic rules

i know that in classic chess when one side runs out of time, he losses if there is any possible checkmate for opponent or if not it is a draw. But in blitz especially in amateur tournaments with no increment it would be harsh to apply the same rules.

For examle this position

It is a clear draw, even theoretical, but black runs out of time. Is he right to claim a draw?

There sould be some differences in rules between classic chess and blitz.

I think the same rules still apply - if black runs out of time in that position white wins. 

As far as I know, the only actual difference between blitz and classical is that you're not required to notate at all in blitz. 

I also am curious about this type of situation. On another server (Chessbase) I reached K+R vs K+R, though I had more than a minute of time left, and my opponent less than 15 seconds. The system automatically (I assume) called the game a draw. When I asked their Support why this happened, all I ever got was an automatic response that my message had been received and they would get back to me within 24 hours. That was several days ago.

It would be nice to be introduced a rule in online chess, maybe 5-moves rule, in such endames rook vs rook, or knight vs knight, or bishop vs bishop, where to be automatically given draw. But on the other hand, in pawn vs pawn endgame it would be impossibe to be automatically established if is draw position or not. Anyway not many people care about online ratings.

But in OTB tournaments, where there is an arbiter that situation could be established easier, if such a rule existed. In my local chessclub the time control is almost always 15 0 without increment, "rapid chess", and if one player losses on time, but is much better in material or there is a drawn engame, then he is allowed to claim a draw. However, once i played a 5 0 blitz tournament and the above rules didn't apply. I reached the diagram position running out of time and the arbiter said it was a win for the opponent.