In general, both moments are called the "bending moment", but you can distinguish them by looking at the member's face - when the force has a direct effect on it, it is the $M_{apply}$; the opposite is the $M_{react}$.
Another way to look it is - when the moment tends to bend the beam segment down (or up) in the same direction as the applied force, it is $M_{apply}$. On the other hand, $M_{react}$ tends to bend/pull the displaced segment back towards the original position.
