The two terms are closely related, but they refer to different things.
An antique is an old piece of furniture, household item, or other similar item, an object that people collect because of its special features, rarity, or personal emotional connection to the object.
On the other hand, antiquity is ancient times; former ages; times long since past; or it can refer to objects or relics of various kinds belonging to ancient times. In building works, they could be parts of ancient structures or artefacts, coins or works of art.