If we want to compare these two terms, we have to first understand their definitions. On the first hand, it is easy define a zero energy building (can be measured in different ways), on the other hand the green building is about efficient use of energy, water and natural materials, and also waste and pollution reduction, which is hard to measure.
Are all net zero energy buildings green buildings? Not really. It is true, that they the achieve the goal of completely or significantly reducing energy use and gas emissions. But zero buildings can not be considered green in other areas, for example using natural materials, waste reduction and others.
However, net zero energy buildings do tend to have a lower ecological impact because they do not require imported energy. Combining these two approaches may be crucial for future sustainability.