Two-dimensional magnetohydrodynamics, forced at (a) large length scales or (b) small length scales, display turbulent, but statistically steady, states with widely different statistical properties. We present a systematic, comparative study of these two cases (a) and (b) by using direct numerical simulations. We find that, in case (a), there is energy equipartition between the magnetic and velocity fields, whereas, in case (b), such equipartition does not exist. By computing various probability distribution functions, we show that case (a) displays extreme events that are much less common in case (b).