Enthalpy shows amount of energy that can be transformed into heat in the reaction (temperature and pressure are important there - they influence on value of enthalpy). It also can tell you about heat effect of the reaction - if enthalpy is posivite, the process is endothermic (it absorbs heat), if enthalpy if negative, the process is exothermic (it generates heat).
Firstly enthalpy is a function of thermodynamic potential. It shows the state of reaction system when it reaches thermodynamic balance. (when enthropy, temperature, pressure and value of reaction don`t change in time).Enthalpy doesn`t depand on the way of reaching final condition.
Heat is not a function of system stage, it`s a function of process. It shows, how enthalpy of reaction changes. Generally it`s an energy that is lost or got by system while it exchanges heat with outside environment. Heat depends on the way of reaching necessary condition.