Poincaré is usually said to be the first one to use homologous. He uses the term in his Analysis situs to mean the relation between manifolds that we nowadays refer to as cobordism or bordism. I have always interpreted his usage to be an extension of the relation of homology (or perspectivity) between triangles in geometry: one can think of a bordism from a manifold M to another N as a (very flexible!) perspectivity from one to the other.