Iceland is relatively green compared to Greenland because of its size, its more southern location and the difference in nearby ocean currents. Greenland is an extremely large island, and while its coastal areas do support some vegetation, its interior is covered in a massive ice sheet up to three kilometers in thickness. Iceland is much smaller, so the moderating effects of the ocean on its climate are greater.
Iceland and Greenland are very close to one another, and both are quite far North. Iceland sits just beneath the Arctic circle, while Greenland extends well into the Arctic circle. Greenland is vastly larger than Iceland, with around 21 times the land area of the smaller island. In addition, Greenland's existing ice sheet both cools the air over the whole island, and reflects radiant heat from the sun, creating a feedback that maintains its cold climate.
Iceland sits directly North of the Atlantic current, which carries warm water to, and thus moderates the climate of much of Europe. What is more, a branch of that current, the Irminger current, flows around the West coast of Iceland. Between the Irminger current and Greenland, however, the East Greenland Current flows Southwest from the Arctic, creating a frigid buffer against the relatively warm waters that benefit Iceland.