Baby is generally referring to the stage in whichthe bird is still unfethered or its feathers are coming in. It should be in the nest and is being cared for completely by the parent bird(s).
A fledgling has all of its feathers and is now spending more time out of the nest learning the ropes as it were from the parents. They are usually starting to self forage but still get fed by the parent.
Juvenile is fully fledged and is on its own but still young (less than a year old usually as juveniles are the ones that fledged that spring/summer). It is often not as big as it will be t its full growth and in some birds the colors will be a bit different until the bird has its first adult molt when its full adult colors will emerge.
I am not an expert so someone else may have a better more complete definition of the terms but this is basically the stages as I understand them.
