thermodynamics - What is the difference between enthalpy (H) and heat (q)?

It seems that in some cases it's the same (that is, $\Delta Q_p=\Delta H$) yet in others they differ. For example, \begin{align} \ce{2H2(g) + O2(g) &->2H2O(l)} & \Delta H &= -572~\mathrm{kJ} \end{align}

The answer for one mole of $\ce{H2O}$ produced is $\mathrm{-572\times 0.5~kJ}$. Is this under the assumption of constant pressure? Therefore it's $\Delta Q_p=\Delta H$?