Jade is a kind of stone. We use the name "jade" for two different sorts of mineral. The first sort is nephrite. This is a form of actinolite (asbestos is a sort of actinolite, too). The second sort is the mineral jadeite, and it is a pyroxene. The first sort (nephrite) is harder than the second sort (jadeite). The first sort (jadeite) has more colors that the second sort (nephrite).
Nephrite is Ca2(Mg, Fe)5Si8O22(OH)2.
Jadeite is NaAlSi2O6.