Wiring is Open Source Software. The PDE (Processing Development Environment) is released under the GNU GPL (General Public License). The export libraries (also known as ‘core’) are released under the GNU LGPL (Lesser General Public License). There’s more information about Wiring and Open Source in the FAQ and more information about the GNU GPL and GNU LGPL at opensource.org.
The Arduino IDE is a cross-platform tool for easy editing and uploading of Arduino programs. The front-end builds on Processing and is written in Java. The code that runs on the board is based on the Wiring API and makes use of the Procyon AVR-LIB.