yes, there is a difference, the gibbs energy represents the maximum non-expansion work, while the Helmholtz energy represents the maximum available work. A cell can use only the gibbs free energy, then, given its internal volume stays the same.

I think the problem wants to see how well we could drive energy out by expansion work (dA) and , by comparison, how well the cells use the chemical energy(dG)

So, from the reaction entropy, enthalpy and gibbs energy you find the temperature( quite odd), and then you write dA=dU-TdS=-TdS, because the temperature inside the cell is constant, so ΔA is straightforward.