Technically using the Arduino name on a clone is a trademark violation. That is why there are so many boards with names like seeeduino, roboduino, etc.
Legitimate clones have no need to use the Arduino name, as they can stand on their own name.
Several of these auctions showing the Arduino name have been cancelled when Massimo Banzi or anyone else associated with the real Arduino group finds them.
For the most part the clones all work just fine, and you will see no difference in using them side by side with an official Arduino board.
Some clone makers just straight out copy the Arduino and add nothing to the design. The best clone makers improve on the design in some way.
Some like the Seeeduino actually break out more of the pins than the official Arduino, some like the EKitsZone MEGA2560 improve the power supply
by replacing the LM358D with a fast response NXP OPAMP, and moving the reset switch to a right angle orientation.
Most clones survive because they are cheaper than the official versions.