I have had some parakeets when I was a kid. Yes, they were in the cages.
You have to understand that most pet birds are pets for generations. They require human care to provide them with food, shelter, and security in order to survive. If you release this kind of pet birds into the wild, the chance is they won't even survive on their own.
On the other hand, there are indeed small number of wild caught birds on the pet bird market. While these wild caught birds are certainly better off in the wild, if you release them into the wrong habitat, they'd still die because they are at the wrong place. For example, if you release some South American Amazon wild birds in Asia, the chance is they won't even find their usual food, and they probably won't even adapt to the local weather. They also have absolutely no idea about the local predators.
In most cases, releasing pet birds into the wild will result in dead birds. Please do not do it unless it is wild caught local birds.
