You're only going to get 120Hz from a source if (a) the original material has 120 frames/sec, or (b) the source device is converting its output to 120Hz. Neither is likely.
»www.pcmag.com/article2/0 ··· 6,00.asp
The 120Hz setting on your TV tells the TV to interpolate the 60Hz source. This is intended to reduce motion blur. Whether or not this is 'better' is subjective.
Meanwhile, the 'little blue box' is reporting what it is getting from the source device.