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?

An Arduino board 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)

Is there a simple rule of thumb to help me decide?

Yes, there is! Think about what you want your project to do. If you can describe it with less than two ‘and’s, get an Arduino. If you need more than two ‘and’s, get a Raspberry Pi.

Examples:
“I want to monitor my plants and have them Tweet me when they need water.” That can best be done by an Arduino.

“I want to monitor my plants and have them Tweet me when they need water and check the National Weather Service, and if the forecast is for fair weather, turn on the irrigation system and if the forecast is for rain, do nothing.” That would best be handled by a Raspberry Pi.

Isn’t that rule of thumb oversimplifying what is actually a much more complex issue?

Yes. That’s what a rule of thumb is.

Look, this is confusing! Just tell me which one I should buy!

An Arduino. It’s a system designed for beginners.

Source:  https://makezine.com/2015/12/04/admittedly-simplistic-guide-raspberry-pi-vs-arduino/