How do the Green's R and L Relations relate with left and right Coset?

Question

How do the Green's R and L Relations relate with left and right Coset? Are there any comparisons? I do know that both tools are used to partition algebraic structures into disjoint substructures. I actually did some paper in characterising generating systems of semigroup but using coset on cyclic semigroups of the over semigroup and arrived at a result similar to some i already seen from those who utilised the restriction of green's L and R relations on subsemigroups of some oversemigroup. In trying to compare both results, i realised that the similarity in the results should be linked to some similarities in these two sets of relations. So the question is, how are these relations compared? Which is implied by the other and how? Thank you.