Before I start, I'm aware that this question may be better suited on the Chemistry or Biology site, but it's my belief that physicists are more likely to have a clear understanding on what certain terms mean, so by all means move the question if you feel like it will get a better response elsewhere.
In Chemistry we learn about this thing called the Gibbs Free Energy (which I understand is borrowed from Thermodynamics). It's pretty simple. $\Delta G < 0$, and the reaction is spontaneous. $\Delta G > 0$, and the reaction is not spontaneous.
Other terms in the equation for Gibbs Free Energy are the total enthalpy change, which I interpret as the amount of energy that the system either takes in or releases, and also the temperature and total change in entropy.
Observe these graphs of an ambiguous 'Energy' plotted against the progress of the reaction:
The idea is the same. Some reactions take in 'Energy,' and the curve ends higher than where it began. Some reaction release 'Energy,' and the curve ends lower than it began. All reactions seem to require an 'Activation Energy' which prevents the reaction from occurring spontaneously.
Notice how the Y-axis has different names, such as Gibbs Free Energy, PE of molecules, and PE. Is Gibbs Free Energy the same or different from PE? I'm not sure anymore. Also, in one graph, the change in Energy is portrayed as $\Delta G$, so a decrease implies spontaniety, and increase implies nonspontaniety. Yet both require an activation energy to proceed.
One more thing to notice is the change in terms. In a Biology context, the terms are Endergonic and Exergonic. In Chemistry, it is Endothermic and Exothermic. Why different terms for the same idea?
I would very greatly appreciate an explanation for this, which has been bugging me for a while.