The labels for chickens and eggs have gotten complicated. Free range, to me, means they can wander around outside wherever. Cage free, means they aren't kept in cages their whole life, but they are still kept within fences outside like most homesteaders do with the portable electric fencing. Joel Salatin uses the term pasture raised chickens, because they are raised in cages on a pasture and moved every day.
But I think you're right that at the very least, "organic" chickens and eggs should mean their food is organic and they aren't pumped full of drugs and stuff. And then cage-free or free-range is a different label describing their living conditions. I don't know either, man, I just want to raise some of my own or know where they are coming from.
I guess that's why (if you care) you need to be very careful about reading food labels. Furthermore going the extra mile to do some added research goes along way since labels are all to often intentionally misleading.
Take the word "lite" for example. Means less fat, however, way more sugar and also what is the process for removing the fat... all the consumer hears is better for you.
Same with alternatives to refined sugar. Apparently sweeteners aren't any better or in some case worse.
I read that aspartame is trying (or there was talk about them trying) to rebrand as "Aminosweet." lol