HDR means that a photo contains more dynamic range than the camera can capture. To create an HDR photo, you normally take two or three shots with different exposure levels and merge them. Tone mapping is the process of converting image tones from a higher range to a lower range.
HDR photography is aimed at overcoming the limitations of cameras that can’t capture the whole dynamic range. Tone mapping is aimed at properly reproducing the dynamic range on the standard display of a device, which is also limited in the colors it can reproduce.