The Greek name for the large storage jar in Hesiod’s original story is pithos.
A pithos was a large earthenware vessel used in the ancient Greek world for storing commodities such as grain, wine, or oil. Hesiod uses this kind of container in the Pandora episode. The object was not the small hinged box shown in many modern illustrations and expressions.
The familiar phrase “Pandora’s box” became established through later translations and adaptations, especially after the Greek pithos was rendered into Latin with a word associated with a box. Because the English phrase is now idiomatic, the original vessel is often overlooked.
An amphora was also a Greek ceramic container, but it normally had two handles and a narrower form. A krater was used for mixing wine and water, while a kylix was a drinking cup. Those vessels are therefore not the specific container in Hesiod’s story.