Emerald was an early green that was released at the same time as Wine and Dark Grey (they are all pretty much the same glossy, smooth cow leather). Emerald is a brighter, vibrant green while Forest green is a bit darker more of a neutral. Forest was released more recently in the last year or two. It is also a cow leather but different in texture.
Envy is somewhere in the middle of Emerald and Forest. Personally I think it is closer to Emerald. It is the exact same hue of green as emerald just a tad darker if that makes sense.