Using both the floor and the bed allows for increased support for your neck and thoracic spine. Performing those exercises on a ball challenges the neck and upper thoracic spine and is therefore not appropriate for people with significant acute pain along those areas. A patient should at least be able to hold their neck in a neutral position to avoid excessive stress while performing arm abduction on a ball.
The ball also adds an element of instability to the entire body, whereas the exercises on the bed and floor do not really challenge your balance or core strength relative to the ball. The ball would not be appropriate for people who have problems with their ankles/feet as they would be required to stabilize themselves through the entire lower kinetic chain before they can do it safely.
Basically, the ball is just a progression of the exercises that should initially be done on the floor/bed. Pending the stage of the patient's recovery and overall status, they can then progress to the ball. Resistance can then be added by carrying free weights or using elastic theraband. Hope this helps!