Those terms suggest a way of raising chickens; let's discover the real definitions. All the above imply that the hens spend their days wandering the grassy pastures of a quiet farm, pecking, scratching and living the life of which every chicken dreams. And who wouldn’t want a vegetarian-fed chicken? We don’t want our chickens to eat other animals. That’s hideous, right?
While it is possible that the eggs contained in cartons bearing those labels truly did live the peaceful and free life, the laws which govern egg production are much more vague and forgiving than most would expect. An egg that labeled as free range must have access to the outdoors. Under that definition, if the farmer opens the pen door and the chickens have potential access to the outdoors--but never goes outside--the eggs meet the labeling requirements of "Free Range." The hens can still live in overcrowded conditions and be fed specific rations of foods designed for most egg production. Since overcrowded hens will peck each other sometimes resulting in death, the hens are often de-beaked while still a chick. Even in free range situations, each bird may have only a square foot of living space and the associated range need only be a dirt run attached to the building.  In fact, the USDA’s definition of “Free Range” or “Free Roaming” is “the poultry has been allowed access to the outside”. 
Cage free birds are simply those birds which are not confined to small cages for their entire egg-producing life. These birds are not required to leave the building nor have access to the outdoors. And since they live as tightly packed as “battery-caged birds” (also known as “factory-farmed birds) they experience the same illness and diseases as the factory-farmed hens. 
Vegetarian-fed may also be labeled as “Grain Fed”. While chicken will eat grains willingly, chickens are actually omnivores. The chickens we now see on farms are descendants of wild game birds; those bird were hunters. That instinct has not been bred out of current breeds. Chickens will happily hunt and eat insects, grubs, and worms, as well as small animals such as mice, voles, and snakes. When the chicken producers only feed grains to the chickens, the chickens are actually denied the foods they want. Also, hens that are able to find and eat such prey have eggs and meat that is more nutritious. 
Organic eggs are from birds fed certified organic foods, can graze on grass and are given vitamin and mineral supplements. They need access to the outdoors, but growers are not required to actually put their chickens outside. The hens are never given antibiotics, but are given vaccinations to help prevent illness. If an illness is found in a flock, the farmer will commonly destroy the entire flock, since there are fewer treatment options because antibiotics are not used. These birds are given healthy foods, but may never be able to hunt and scratch as driven by their nature. 
So What Should You Look For?
When the words “pasture raised” are on the label, it indicates that hens actually lived in a pasture, had access to living grass, chased bugs and scratched for worms. The specifics vary about how the least square feet of living space per bird, but this is by far the best possible option for eggs and meat birds. It is still possible that pasture raised birds still lived a life far from pastoral, because many birds could be kept in a single confined field. 
We now know that pasture raised eggs are the preferred choice, but are they actually healthier? Mother Earth News compared pasture hen eggs with more conventional eggs in 2007. They have the same number of calories, but chickens raised on pasture produce eggs which have 33% less cholesterol, 25% less saturated fat, 66% more Vitamin A, twice the Omega-3 fatty acids, three times the Vitamin E and 7 times more beta carotene.  Are those differences enough to keep you healthier? Maybe, maybe not. But because these hens were able to live more naturally, their eggs tend are more nutritious.
The color of the eggs are meaningless in terms of nutrition. Brown eggs are no more nutritious than white; they just come from hens that lay brown (or green, blue or speckled) eggs. There is only one other way to know that you are eating the healthiest possible eggs, from hens living the most natural life. If you have your own backyard flock of laying hens, you are in control of the eggs on your table.
Like anything in life, the key to success is knowledge. The next time you shop for eggs, you know what to look for and what those various labels may mean.
All photographs Trevor LaRene, 2015