We report the result of new experiments on a granular medium sheared in a Couette geometry. We investigate in particular the dependence of the resulting stick-slip patterns on the imposed shear rate. A model equation based on a stochastic description of the internal forces of the granular medium allows us to recover the experimental results and unveils similarities between the stick slip motion and the Barkhausen noise emitted by a ferromagnet during a hysteresis cycle. We show that, because of the stochastic nature of forces in the granular medium, there is indeed a correspondence in the statistical properties between shear rate fluctuations in granular media and displacement of magnetic domain walls under a varying external field. The main difference between the two systems consists of a characteristic behavior on the part of the granular medium, but which is not exhibited by the Barkhausen effect. The stochastic model proposed allows us to ascribe this behavior to the moment of inertia of the plate and, on the basis of available data from the statistical properties of friction in solid-on-solid systems and in polymer mono-layers, suggests the possibility of describing a larger class of driven instabilities in terms of similar general mechanisms.