Processing is an open source programming language and environment for people who want to program images, animation, and sound. It is used by students, artists, designers, architects, researchers, and hobbyists for learning, prototyping, and production. Processing is built on Java, so there are many similarities between these two languages. Processing is used to create programs that run on a PC.
BasicX is the language written for the Netmedia BasicX family of microcontrollers.
The Wiring environment is written in C and C++. Programs written in Wiring are also translated to C++ and then run as C++ programs in the Wiring hardware.
Large distinctions between Wiring and C/C++ are the Wiring API and libraries and a simplified programming style that doesn't require users to understand more advanced concepts like classes, objects, pointers (while still making them accessible for advanced users). Such technical details must be specifically programmed in C/C++, but are integrated into Wiring, making programs shorter and easier to read.