Kin selection and group selection were once seen as competing explanatory hypotheses but now tend to be seen as equivalent ways of describing the same basic idea. Yet this 'equivalence thesis' seems not to have brought proponents of kin selection and group selection any closer together. This may be because the equivalence thesis merely shows the equivalence of two statistical formalisms without saying anything about causality. W.D. Hamilton was the first to derive an equivalence result of this type. Yet Hamilton was aware of its limitations, and saw that, while illuminating, it papered over some biologically important distinctions. Attending to these distinctions leads to the concept of 'K-G space', which helps us see where the biological disagreements between proponents of kin selection and group selection really lie.