difference between android gradle plugin and gradle

Even if you have written the same java source code for a java project and android project, the way they are built and executed completely differs from each other.
Java project sources compiles to byte codes (.class files) and runs on JVM (java virtual machine). Android project sources compiles to Dalvik byte codes (.dex files) and runs on DVM (Dalvik Virtual Machine). And both of these virtual machine have different ways of executing commands.

Android projects have many platform specific steps when building application that standard Java applications does not have. (like packaging as apk, automatic signing, project flavors management, minimum API level) With the addition of Android Gradle plugin these differences can be applied more easily and in a more refined way. (So building Android apps becomes easier for everyone).

Gradle is the build system.

You can use it with a lot of plugins. One of these is the Android Gradle plugin.
It is used to provide processes and configurable settings that are specific to building and testing Android applications.