Probably the jasper of the ancients included stones which would now be classed as chalcedony, and the emerald-like jasper may have been akin to the modern chrysoprase.
From the en.wikipedia.org
There are more than 80 different precious stones to choose from, ranging from the standard amethyst, tiger's-eye and lapis lazuli to the more grand leopard jasper, chrysoprase and mother-of-pearl.