Ramon, the words can be synonymous. For example, the phrase "She is wearing pants" in portuguese we could say: "Ela está vestindo calças" or "Ela está usando calças".
But the verb "vestir" can also indicate the act of dressing up / putting clothes on. Ex.: "Ela está se vestindo". In this case, I couldn't use the verb "usar", because it means the clothes are already putted on.
The verb "usar" is also used in other cases, and could be transleted by the verb "to use" in English. However, the verb "vestir" is just associated with clothes.