Arduino Derivative Boards
'Arduino-Based' boards are boards that have been designed and built using the Arduino footprint, and / or the Arduino bootloader. They can usually be programmed via the Arduino IDE. Just because they're not made by Arduino themselves doesn't mean that they're illegal copies. Quite often 'clone' boards are supported by Arduino - It's all part of the 'Open Source' movement. Arduino-Based boards usually offer functionality or performance levels that Arduino have not chosen to offer in their genuine boards. Occasionally, they're even cheaper.