A music bed, also known as underscore, is a term that originates from the radio. It is understood as the background music or jingle behind an announcement, for example. Although both terms are basically synonyms, the difference lies therein, in that the latter is background music specifically created for a project, usually a movie or a TV show. Such music is usually constant in mood, and is played as a loop.
Examples of these are a number of songs and music themes from the 1980s. MTV was relatively new at the time, so that songs were promoted through soap operas. Kissing scene? There was a theme or a song people identified it with, as was the case of Bo and Hope in the long running American soap opera Days of Our Lives.