[rentj]

I read in my physical chemistry textbook that Gibbs energy ΔG = ΔH - TΔS, however later in the book, I found another quantity, which is reaction Gibbs energy, denoted with Δ_rG. I am confused between the differences since the book stated that the reaction Gibbs energy is the slope of the Gibbs energy plotted against the extent of the reaction, dξ. It is said that if the reaction Gibbs energy, Δ_rG < 0, the reaction is spontaneous or exergonic. However in other sources, I saw that if the change in Gibbs energy ΔG < 0, the reaction is also exergonic. Isn't that mean that Δ_rG and ΔG are both the same quantity? Thank you.

[mjc123]

I'd recommend looking at this thread: https://www.chemicalforums.com/index.php?topic=87048.0, and the thread I quote inside it.
Note that there are some differences in notation between different sources.
ΔG < 0 (as you define ΔG) means that the conversion of pure A to pure B is exergonic.
Δ_rG < 0 (as you define Δ_rG) means that it is spontaneous for the reaction to proceed in the direction of increasing ξ from where it is.
A graph such as in those threads should make this clearer.