You can install both processing and arduino without any problem. Those are two really different softwares. arduino is just for programming the arduino board (or boarduino an any other equivalent). it allows you to write the software that goes on the chip and to debug it. Processing on the other end doesn't have any GUI or whatever, it's just a software that allows you to use a "simplified" version of Java, so that you can code software without virtually knowing Java. It doesn't allows you to program the arduino, but you can read and write data to it, to light some leds or analyze what comes from some sensors. With processing, you can "process" these datas and have some kind of interaction with the computer screen / keyboard / mouse. Maybe a "real" exemple would help you : in processing, you can write a software with some buttons, the user clicks one of these buttons, processing sends it to the arduino board, and a Led lights up. For the led to light up, you have to write the proper code in the Arduino IDE and upload it to the board via the same Arduino IDE.