the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
The terms mubâh and mustahabb both refer to Islamic legal rulings that define the legal context of the actions that a person might perform.
The term mubâh means “permissible”. If a given action is classified as being mubâh, then is something that we are not called upon by Islamic Law to either do or refrain from. There is no inherent reward for doing it or abstaining from it.
The term mustahabb means “something liked”. If a given action is classified as being mustahabb, it is something that we are called upon by Islamic Law to do but that we are not obliged to do. If we do it, we are eligible for reward but if we abstain from it we are not liable for punishment.
Actions that are mubâh and mustahabb both have in common the fact that they are lawful for us to engage in. They also have in common that they are not obligations. (An action that is obligatory upon us is described as being wâjib.)
They differ in that engaging in something that is mustahabb is an act of piety worthy of reward, while this is not the case for something that is mubâh.
Source: Islam Today