The difference is control. A person knows that if he disables a desktop client, he won't be receiving any messages.
A phone user expects that messages would be displayed to him in notifications when received. One does not expect to be cut off communications because he had pressed a 'home' button, but it's what happens, and a user does not have any control to prevent it from happening.
A phone user expects that messages would be displayed to him in notifications when received. One does not expect to be cut off communications because he had pressed a 'home' button, but it's what happens, and a user does not have any control to prevent it from happening.