  We elucidate a long-standing puzzle about the non-equilibrium universality
classes describing self-organized criticality in sandpile models. We show that
depinning transitions of linear interfaces in random media and absorbing phase
transitions (with a conserved non-diffusive field) are two equivalent languages
to describe sandpile criticality. This is so despite the fact that local
roughening properties can be radically different in the two pictures, as
explained here. Experimental implications of our work as well as promising
paths for future theoretical investigations are also discussed.
