Can someone tell me the TRUE difference?
To complement the other answers here regarding the distinction between service and AsyncTask, it is also worth noting[0]:
Services tend to be things that describes a significant part of your application - rather than an AsyncTask which is typically contributes to an Activity and/or improves UI responsiveness. As well as improving code clarity Services can also be shared with other applications, providing clear interfaces between your app and the outside world.
Rather than a book I would say the developer guide has lots of good answers.
[0] Source: http://developer.android.com/reference/android/app/Service.html#WhatIsAService