Homophones are words that sound the same but have different meanings and spellings, like see and sea. Homonmys are words that are spelled and pronounced the same but have different meanings, like cold describing temperature, illness, or unfriendliness. The document provides examples of homophones like fair and fare and homonyms like glasses referring to drinking vessels or eyewear. It explains that homophones can lead to spelling errors while homonyms take on different parts of speech.