The Bel and the deciBel are just the Logs10 of ratios of Power and not related to any particular field of Engineering or any particular signal. When referred to sound, they are used relative to a notional 'threshold of hearing' of 0dB.
Because our hearing is a complicated and subjective mechanism, to get a better idea of relative loudness of sounds, including background random noise, it was found to be useful to measure the total Power through a band pass filter which was designed to mimic the human audio frequency response. The dBA scale (and the others) is one of the attempts to give a single, meaningful number to represent the perceived loudness of a sound (along with lots of caveats as to the real suitability of the number).