The grass is always greener on the other side of the fence.

This saying is used when we think that what others have is better than what we have. We also say to be green with envy or to be bitten by the green-eyed monster to describe an envious or jealous person.

But to be as green as grass  can mean to be very green in colour or can also refer to a naïve and inexperienced person: The new teacher is as green as grass and believes anything you say. 

Other expressions with «green»  include:

not let the grass grow under (one’s) feet means to be very active: Maria doesn’t let the grass grow under her feet. She goes to Japanese, Pilates and cookery classes, as well as working six days a week. 

the grass roots of an organization, often a political party, refers to the ordinary members as opposed to the leaders. In many parties the leadership is out of touch with the grass roots.

 hear the grass grow means that it is so quiet that you can hear anything: It was so silent in the library you could hear the grass grow.