These words are often tossed around by teachers and linguists. What do they really mean? The prefix homo- comes from the Greek word homós which meant “one and the same.” So all of these words describe some types of sameness.
Homographs are words that are spelled alike, but have different meanings and sometimes different pronunciations. The root graph comes from the Greek word meaning “drawn or written,” thus these terms are written the same. For example, stalk is both a plant stem and a verb meaning to pursue stealthily. Homographs also have different etymologies.
Not all words that are spelled the same are pronounced identically, so they may be homographs without being homophones, e.g., lead as a metal and as the verb “to show the way.” Homophones are words that are pronounced the same but are different in spelling and meaning. In this case the combining from phone comes from the Greek word phōnḗ meaning “voice.” One commonly confused trio of homophones is to, two, and too.
Homonyms are words spelled or pronounced alike but different in meaning. Since homonym is used to (ambiguously) describe either a homograph or homophone, it can cause confusion, though it is often heard in classrooms in early grades. The root -nym simply means “word” or “name,” so it applies more broadly than its counterparts.