Doesnt sound like the same thing. 1080p, 1080i, 720p, and 480i are resolutions (vertical number of pixels followed by an i for interlaced or p for progessive mode)
120 probably refers to refresh rate of 120Hz, meaning 120 frames are displayed per second. The faster the refresh rate, the less blurry movement on screen appears.
Most likely, you've bought a 1080p TV (which probably also supports 720p and 480i, as most do) that has a refresh rate of 120Hz. TV might simply be saying that it's displaying HD content at 1080p and regular definition content at a psuedo-480p (a 480i singal that is rendered across two frames due to the "double rate" of 120Hz over the normal 60Hz rate)