What's the difference between a clone and a counterfeit Arduino?
The difference is simple: 

Clones don't say "Arduino," where counterfeits do

If I were to create 200 boards all labeled "Arduino UNO R3," it would be a counterfeit. If I were to call them "Happyduino," it would be a clone. 



Note: You can still write Happyduino (Arduino Compatible) on your product. Here's a quote from the Arduino FAQ section


  Not okay:
  
  
  Arduino Xxxxxx
  Xxxxxx Arduino
  Arduino Compatible Xxxxxx - use "Xxxxxx (Arduino-Compatible)" instead
  
  
  Okay:
  
  
  Xxxxxx for Arduino - products that work with official Arduino boards    (e.g. shields or kits)
  Xxxxxx (Arduino-Compatible) - variations and clones which are    software and hardware compatible
  
  
  Note that while we don't attempt to restrict uses of the "duino"
  suffix, its use causes the Italians on the team to cringe (apparently
  it sounds terrible); you might want to avoid it. (It's also
  trademarked by a Hungarian company.)