There are two different kinds of green lentils: French Green or Puy. The only significant difference is region of growth. Puy lentils are grown specially in the French town of Puy. More often than not, the green lentils you buy in the grocery store are just that, plain green lentils. Green lentils are more comparable to brown in that they hold their shape and texture better than the red. However, green lentils tend to have a bit stronger of a taste compared to the brown lentils.
These lentils are great as a dish on their own, used in stews, or even a salad topper. The Kitchn offers great advice on how to cook lentils (and a warning that the older the lentils, the longer the cook time. )
My Recipes for Green Lentils