I think green machines have functionality to allow you to make advance reservations for seats on express trains - i.e. same functionality as the ticket offices, which have green signs - midori no madoguchi (literally: green counters). The ticket machines will probably have more limited functionality - allowing you to pay fares to your destination without reservation functionality etc.

On some platforms, you'll also find green colored machines that sell upgrades for "Green Car" (premium class) seats on some services that depart from the same platform. This is an entirely different beast.