Conventional TV sources are (at best) ~60Hz (59.94 in former NTSC land, 50.00 in former PAL land). Movies are 24 fps. A lot of TV is also interlaced, so you have to do something about that, and you'll end up with, at best, ~60fps as a result of that process. If you turn on the "120Hz mode", yes, it just upconverts. It's also handy if you feed the TV a native 24p signal for a movie, since 24 evenly divides 120 (but not 60), so you can avoid a 3:2 pulldown.
Computers, however, can easily do 120Hz refresh rates (and even higher - let me assure you that 160Hz just looks wrong, too, as it's TOO smooth). Most TVs won't accept it if you just naively set your PC to 120Hz and hook the cable up, but if you instead tell the TV that you're sending it a "3D" signal that isn't actually 3D (it's just a chain of progressive frames at 120Hz) and don't bother putting on the glasses, you can get 120Hz refresh out of a lot of modern 3D-capable TVs. Handy little trick. You may have to adjust whether left or right comes before/after the other since some TVs do it in different orders from others. Obviously this only works on TVs with shutter glasses, not passive polarized glasses.