You're giving away Duke Stars for this? :)
IDE: Integrated Development Environment
The J2SDK comes in the form of the compiler, javac and the JVM, java ( along with classes etc ). To code with this, you need some sort of editor, like notepad or edit in MS-DOS. Once you finish typing, you then compile and run. If you encounter errors, you might want to debug using another tool.
An IDE combines all of these ( hence Integrated ) into one application ( the Environment ) for development. At the very least, you'd expect an IDE to have an editor, some way to compile and run and possibly debug your code. Along with this, you may get a version control system too.
Examples are NetBeans, Eclipse for Java and Microsoft Visual Studio for VB, VC++ etc. An old IDE would be Borland's Turbo C.
Plugin: Also known as addin or addon. These are small program that 'add-on' to the main host program like say, your IDE or your browser and add some functionality it. For example, Google Toolbar would be a plugin for Firefox or IE. The NetBeans Mobility pack would be a plugin for NetBeans.
More here:
http://en.wikipedia.org/wiki/Integrated_development_environment
http://en.wikipedia.org/wiki/Plugin