简单翻译:

  V4用于1.6到更高的API使用。

V7是2.1到更高的API使用，其中包含ACtionBar。

V13是3.2到更高的API的使用。

原文：

v4 Support Library

This library is designed to be used with Android 1.6 (API level 4) and higher. It includes 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 included 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.