What's the difference between ΔG° and ΔG°'?
The prime usually denotes a standard free energy that corresponds to an apparent equilibrium constant where the concentration (or activity) of one or more constituents is held constant.

For example, for $\ce{HA &lt;=&gt;A- + H+}$ the equilibrium constant is $K=\frac{[\ce{A-}][\ce{H+}]}{[\ce{HA}]}$ and the corresponding standard free energy change is $\Delta G^\circ=-RT \ln(K)$. If you know the value of $K$ and the start concentration of $\ce{HA}$ then you can compute the equilibrium concentrations of $\ce{HA}$, $\ce{A-}$, and $\ce{H+}$.

However, if the pH is held constant then $[\ce{H+}]$ is no longer a free variable and the apparent equilibrium constant is $K'=\frac{[\ce{A-}]}{[\ce{HA}]}$ and the corresponding standard free energy change is $\Delta G'^\circ=-RT \ln(K')$. So $\Delta G'^\circ=-RT \ln(K/[\ce{H+}])=\Delta G^\circ+RT\ln[\ce{H+}]$

In biochemistry there is often several important constituents in addition to  $\ce{H+}$ that are held constant such as $\ce{Mg++}$, phosphate, etc.