You can have a two sample t-test too... for two t-distributions. Or more sophisticated tests (including K-S) for t vs norm, but the problem is, you need very large sample to distinguish between distributions that differ mostly in the higher moments (ie, kurtosis). That may not sound particularly interesting (who cares if it's a t with large degrees of freedom vs normal - good enough for most use) in the two distribution case here,... ... but what happens if the the realizations are from the residuals of two competing trading signal models
Just reporting back to the thread contributors ... Another simple, intuitive method of comparing distributions seems to be the Q-Q plot ... http://en.wikipedia.org/wiki/Q-Q_plot R produces these very easily, and it seems to me to be an excellent way to get a good intuitive sense of how the two distributions differ. Also, with a series of Q-Q plots over time, it's easy to get a good sense of how this relationship evolves over time, too.