The Arduino Nano is a small, complete, and breadboard-friendly board based on the ATmega328 (Arduino Nano 3.x). It has more or less the same functionality of the Arduino Duemilanove, but in a different package. It lacks only a DC power jack, and works with a Mini-B USB cable instead of a standard one.
Arduino Pro Mini is minimal design approach to Arduino. This is a 3.3V and 5V Arduino running the 8MHz bootloader. Arduino Pro Mini does not come with connectors populated so that you can solder in any connector or wire with any orientation you need. We recommend first time Arduino users start with the Uno R3. It’s a great board that will get you up and running quickly. The Arduino Pro series is meant for users that understand the limitations of system voltage (3.3V) and (5V), lack of connectors, and USB off board.