Earbuds are placed inside one's ear so the amount of air that is needed is very small. This means that earbuds can get away with a small, less powerful magnet and a small coil. And due to the tight space concentrate, earbuds as they are now, are forced to only have one cone. This also makes the earbuds as light as possible.
Headphones operate near identical to loudspeakers. The big difference is simply the scale. Loudspeakers, like those seen at giant concerts need to vibrate a lot of air to carry the sound wave. Loud speakers can also use multiple sized cones to best fit the type of vibration.