Differences between Android support V3 v7 v13
Simple translation:
V4 is used for APIs from 1.6 to higher.
V7 is used by APIs from 2.1 to higher, including ACtionBar.
V13 is the use of APIs from 3.2 to higher.
Original article:
V4 Support Library
This library is designed to be used with Android 1.6 (API level 4) and higher. it hosts des the largest set of APIs compared to the other libraries, including support for application components, user interface features, accessibility, data handling, network connectivity, and programming utilities.
V7 Libraries
There are several libraries designed to be used with Android 2.1 (API level 7) and higher. These libraries provide specific feature sets and can be encoded in your application independently from each other.
V7 appcompat library
This library adds support for the Action Bar user interface design pattern.
Note:
This library depends on the v4 Support Library. If you are using Ant or Eclipse, make sure you include the v4 Support Library as part of this library's classpath.
So yes you need both jars if you want to use v7.
Read more about Support Library Features
Update for android-support-v13.jar
V13 Support Library
This library is designed to be used for Android 3.2 (API level 13) and higher. It adds support for the Fragment user interface pattern with the (FragmentCompat) class and additional fragment support classes
When you see the package details it has a class FragmentCompat as given in definition. So it has not the all classes of appcompat library.