  We propose a spin model with quenched disorder which exhibits in slow driving
two drastically different types of critical nonequilibrium steady states. One
of them corresponds to classical criticality requiring fine-tuning of the
disorder. The other is a self-organized criticality which is insensitive to
disorder. The crossover between the two types of criticality is determined by
the mode of driving. As one moves from "soft" to "hard" driving the
universality class of the critical point changes from a classical
order-disorder to a quenched Edwards-Wilkinson universality class. The model is
viewed as prototypical for a broad class of physical phenomena ranging from
magnetism to earthquakes.
