Homonyms are words that have the same spelling and pronunciation, but different meanings. It can get difficult when words sound the same but can mean different things. This is where context clues come into play. Even though one word can have multiple meanings, the rest of the sentence should give you a clue of what is being discussed.
Homographs are words that have the same spelling, but have different pronunciations and meanings. As far as our speech, this makes homographs easy to distinguish. However, when we're reading, we have to be careful to rely on our context clues to give us a clue of what the meaning is for the word.