A homonym is not the same word. Homonyms include both homographs, which are still two different words with different meanings, just spelled the same way (e.g lead[verb] and lead[noun]), and homophones, which are also still two different words with different meanings, just pronounced the same way (e.g. there and their). That said, homonyms also includes word pairs that are both homographs and homophones like "bat", being the animal, the verb, and the baseball equipment (presumably among other uses).