Enthalpy is the maximum energy in a system. Gibbs free energy G = H - TS, where H is the enthalpy of the system. Due to an inherent disorder in the system (entropy, S) which cannot be converted to useful work, we have to subtract it from H
It was good you made this reply since it brings out your misunderstanding of the subject.
Woody told you true and was only trying to help.
I think he deserves thanks for that, don't you?
If heat content (enthalpy) is the maximum energy of a system I suggest you stand in front of a cannonball travelling at 200 Kilometers per hour and try to convince me that it has the same energy as a similar cannonball standing quietly by your left foot, but is at the same temperature as the travelling one.
A bit of mathematics for you.
yes, dG = dH - TdS with appropriate sign conventions.
BUT
T is always positive, and if dS is positive the process can be spontaneous.
If dH is negative (ie the process evolves heat) then dH and -Tds add and this makes dG more negative but greater in absolute value than dH.
This is the condition for a spontaneous process - that dG is negative (evolves energy)
As regards to your question, Gibbs free energy is no different than any other sort of energy.
It is a property of a body or system, a form of accounting, not a real entity like a cannonball. The caloric theory was discredited more than 250 years ago.
As an aside note that eneergy is not a conserved property under Einstinian relativity, the first law holds within any given frame but the energy sum will be different from frame to frame.