A no-hitter still records as an official no hitter even if the pitcher walks some of the batters, right? Does the no-hitter still stand if a run comes in by players that were walked onto base? That has to be rare, but it must happen once in a while. Does the no-hitter status get wiped out if a run comes in?
A shut-out is a scoreless game. So there can be hits, but no runs?
Are both equal in terms of pitching difficulty in your estimation? Do most shut-outs actually record very few hits, or are there any examples that you know where there were actually lots of hits, but the pitcher still managed a scoreless game?