Aristotle has just finished discussing homonyms at the start of the Categories. Next, he discusses words that are identical in meaning.
When things have the name in common and the definition of being which corresponds to the name is the same, they are called synonymous. Thus, for example, both a man and an ox are animals. Each of these is called, by a common name, an animal, and the definition of being is also the same- for if one is to give the definition of each what being an animal is for each of them one will give the same definition.
When two things have a name that is the same, and the definition of that name is also the same, then the names are synonyms. We call an ox animal and a man animal and mean exactly the same thing when we use the word animal. We know this because what it means for a man to be an animal and what it means for an ox to be an animal is the same thing. Therefore, the definition of animal as applied to oxes and men is the same.
In modern use, we do not divide names that are identical into homonyms and synonyms. Instead, we use those categories as different ways of dividing words in general. This means that some synonyms such as quiet and silent are different words even though the meaning is identical.
Next, Aristotle discusses the final category of paronymous words.