Advantage of backward and symmetric Gauss-Seidel iteration

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What is the actual use case of a backward Gauss-Seidel iteration and the symmetric Gauss-Seidel iteration? Are there specific matrices or matrix properties at which I can identify if I have to use forward, backward or symmetric Gauss-Seidel?
I have seen in algebraic multigrid that the restriction uses forward Gauss-Seidel as relaxation whereas the prolongation uses backward Gauss-Seidel. Is there a specific reason for that?