Conceptual understanding of semiconductors - definition of holes
The electron current is due to movement of free electrons in the conduction band (CB) and the hole current is due to the movement of holes/electrons in the valence band (VB). Hence the mobility of holes in VB and electrons in CB are different as well. Hence the respective current densities are different too. Since both contribute to the net current flow in a semiconductor, we add them up. 

$$J = J_p + J_n = e(nu_n + pu_p) $$

Where n, p are electron and hole concentrations.

\$u_p\$ and \$u_n\$ are respective mobilities.