Jasper was originally applied to every green translucent stone. It now means opaque red chalcedony (although you can have jasper of other colours as well). The derivation shows that it was precious, possibly any precious stone. Now it tends to be used of any patterned or plain chalcedony that no-one has a better name for, and it's cheap!
Archaeologists have found jasper (in the modern sense) amulets in Japan, Mexico and Egypt. Assyrian and Babylonian seals were sometimes made of jasper.