WHAT IS THE DIFFERENCE BETWEEN THE TWO?
An Arduino is a microcontroller motherboard. A microcontroller is a simple computer that can run one program at a time, over and over again. It is very easy to use.
A Raspberry Pi is a general-purpose computer, usually with a Linux operating system, and the ability to run multiple programs. It is more complicated to use than an Arduino.
WHAT WOULD I USE EACH FOR?
Use an Arduino and Relays to Control AC Lights and Appliances
High-Speed Splash Photography Rig with Arduino
Build Your Own Arduino Weather Station
Arduino is best used for simple repetitive tasks: opening and closing a garage door, reading the outside temperature and reporting it to Twitter, driving a simple robot.
Raspberry Pi is best used when you need a full-fledged computer: driving a more complicated robot, performing multiple tasks, doing intense calculations (as for Bitcoin or encryption)