I have plenty of explanations of it 'in English' of what the Gibbs/Helmholtz equation actually gives, but none of it is still clear to me...
G = H - TS => dG =
dH - d(TS)
A = U - TS => dA =
dU -d(TS)
We denote energy change for an open system using: dH = Q + W
We denote energy change for a close system using : dU = Q + W
Hence, dH for an open system is equivalent to dU for a close system
Hence, you can regard the Helmholtz Equation as the equivalent of the Gibb equation for a close system. The Gibb equation applies for an open system. G describes the free energy available in an open system, whereas the Helmholtz equation describes free energy available in a close system.