Certified: Manufactured for and sold through the Arduino organisation.
Clones: Use most or all of the Arduino schematics and board patterns but branded differently. Quite legitimate as long as they are not claimed to be an original Arduino.
Derivatives: Enhancements or at least variations to the circuit, distinctly branded. Quite legitimate as long as they are not claimed to be an original Arduino.
Counterfeit: Use most or all of the Arduino schematics and board patterns but branded to imitate the genuine product.