Were the Papal States Vatican City in the 14th century?

Vatican City did not exist as an entity until 1929 with the signing of the Lateran treaty. Before that, the Vatican was merely a neighborhood in Rome where much of the Catholic Church was located. All of central Italy, including Rome, were included in the Papal States.

For a complete discussion of the Papal States see the article in the Catholic Encyclopedia at the link below. The Papal States were the largest portion of Italy, almost the entire central portion up until the 14th century. It was during the Avignon crisis that the Papal States started to unravel, but Vatican City has always been a part of that.