Android Studio is built off of the codebase[0] from IntelliJ 13. The JetBrains products like RubyMine, WebStorm, and seem to be built off of the same core IDE with plugins for languages/platforms and features. So most of the functionality is really just in plugins, and of course IntelliJ probably offers additional Android development functionality for a price.

[0] http://www.jetbrains.org/pages/viewpage.action?pageId=983211

Android Studio is a fork of the OSS IDEA by Google. IntelliJ IDEA is the version released by the actual company and is not affiliated with Google.

IntelliJ IDEA and Android Studio FAQ: http://bit.ly/1d7U0Kg

Q: Is Android Studio a fork of IntelliJ IDEA?

A: No. Android Studio and the Android plugin for IntelliJ IDEA are built from the same code, and all of the changes in Android Studio are, and will continue to be, available in IntelliJ IDEA releases.

It's a fork in the sense that it's a fork of the IntelliJ repo with Google/Android related assets added. So it's more of a branding fork than a code fork, but since its in a different repo I'd still call it a fork. But it's just terminology I guess.

But that ships with IntelliJ IDEA, so it isn't a fork. Android Studio is a subset of IDEA 13.

These resources might help:

IntelliJ IDEA is the base for Android Studio, the new IDE for Android developers: http://bit.ly/1jN1bgb

IntelliJ IDEA and Android Studio FAQ: http://bit.ly/1d7U0Kg