NC and SC are, roughly, the class of problems decidable by shallow circuits of polynomial size and the class of problems decidable by narrow circuits of polynomial size, respectively. They are both subsets of P.
As far as I know, we don't know whether either of the two classes includes the other (at least that was the situation in 1989, according to Dymond and Cook's paper "Complexity Theory of Parallel Time and Hardware").
What are (natural or practical) problems we know are in SC but don't know whether they are in NC?
