To clear up any confusion we first need to define some terminology:
-Vatican City is a city-state with clearly defined borders. It is an independent country surrounded by Italy, and presided over by the Holy See (the Catholic church’s jurisdiction), with its own leader (the Pope), security force (the Swiss Guards), post office, etc.
-Inside the walled borders of Vatican City are the Vatican Museums. These museums are vast and contain huge collections of art and stunning antiquities, and the world-famous Sistine Chapel.
-There is also a small part of the Vatican city that is outside the walls and may be wandered into from the street. In this space is St. Peter’s Square and St. Peter’s Basilica which is the world’s largest church.
When someone asks “are you going to visit the Vatican while you’re in Rome?” they likely mean the Vatican Museums.
The Vatican Museums require you to buy a simple entrance ticket and take about four hours to go through, even to scratch the surface of the 8 miles of corridors, and to visit the Sistine Chapel.
St Peter’s Basilica is free to enter, but the lines can sometimes be 30-40 minutes long. With this inexpensive ticket you can bypass the lines and enjoy an interpretive audio commentary of the wonders within the church.
