Let $S_X$ be the barycentric subdivision operator of a topological space $X$ in singular theory. (The one standard algebraic topology texts such as Hatcher and Munkres) There is also a machinery so called barycentric subdivision in simplicial theory. The idea of constructions are the same, but they are different. I wonder if there is a reason not to distinguish them in terminologies.
So, my question is whether $S_X$ is just a machinery to prove Excision theorem. I skimmed my texts, but I clould not find $S_X$ after the proof of excision theorem.