The Vatican Museums are pluralized for a reason—within the complex there are several individual museums. It’s easy for them to blur together as you wander through, but different collections are housed under different “museum” names. One such collection is the Chiaramonti Museum, sometimes called the Chiaramonti Gallery (Galleria Chiaramonti in Italian). The name comes from Pope Pius VII, who established the museum in 1807 and gave the museum his family name (prior to becoming Pope, of course).
The Chiaramonti Museum is primarily a sculpture gallery, including a large number of Roman busts and statues, stone tablets with inscriptions, stone sarcophagi, and decorative friezes. There are two sub-sections of the museum called the Braccio Nuovo (New Wing), with its Roman statues and Roman copies of Greek statues, and the Galeria Lapidaria, full of stone tablets with inscriptions. The latter is not open to the public without prior special arrangement. Much of the collection in the Chiaramonti Gallery is on display in a long corridor with arched ceilings.
The complex of Vatican Museums dates back to the time of Pope Clement XIV in the mid-18th century, so the Chiaramonti Museum is one of the older museums in Vatican City.