There are three primary distinctions of auditory agnosia. Linguistic (or verbal information or Wernicke's) agnosia indicates that the subject can't comprehend words, although they can understand words using sign language and words from reading books, and are themselves capable of speech (and even of deriving meaning from non-linguistic communication e.g. body language) the particular sounds associated to each word are meaningless.
Classical (or pure) auditory agnosia is an inability to process environmental sounds, such as animal noises, industrial noises, or the like. An airplane roaring overhead would not be understood to be related to the idea of "airplane" -- indeed, the person would not even think to look up.
Interpretive or receptive agnosia (amusia) is an inability to understand music. The term 'Amusic' covers a broad spectrum: from those with a mere deficit of rhythmic ability (mild dysrythmia), to those with heavy all-encompassing Amusia, including the recently coined "Distimbria"; sufferers regard music as simply "noise", often compared to some form of other noise. Vocal singing can be understood, but is simply seen as "odd tone of voice". The standard is considered to be that amusics with a "normal" intensity of amusia are cortically unable to distinguish pitch changes of less than three semitones. They may appreciate or enjoy listening to or performing music, but some can not tolerate it or find it irritating.
NB. These are somewhat ambiguous definitions, and are changing all the time as they are updated to fit the current neuropsychological model of the physiological behaviours and manifestations of these deficits, and cannot therefore be considered a concrete meaning.