Counterfeit: the vendor says/implies that the Arduino board is produced by Arduino/Genuino, an "original", but it is not. The screen-print is the same, but looking closer at the components and PCB there are some differences. You think you can turn to Arduino/Genuino for product support but you cannot.
Clone: the vendor states that the board is a "compatible copy", uses all the open-source bill-of-material, schematics, etc, (or slightly changed for cheaper components) when produced, and it is obviously not produced by Arduino/Genuino. You know that you cannot turn to Arduino/Genuino for product support.