Sensory processing disorder can cause over or under reactions to sensory input, like loud sound. Can those afflicted with this disorder be okay from a particular sound played at a particular volume but react to a different sound played at the same volume? How can this disorder be differentiated from a phobia or various other disorders?
To answer your first question, I am fairly certain that those afflicted with this disorder, or more directly, a person who cannot tolerate a particular sound at a particular volume but react differently (find tolerable) to another sound even at the same volume, is definitely possible. For example, to provide a concrete example, let's assume an individual with SPD throws a tantrum when he hears a note out-of-tune, but can tolerate in-tune notes, regardless of volume. Some associate SPD with Autism Spectrum Disorders  (even one of the symptoms in the DSM-IV-TR for Asperger Disorder  make note of sensory hypersensitivity and hyposensitivity). In the example I mentioned, I don't think one would use the term "phobia" to characterize the reactive behavior to the stimuli. And someone with auditory SPD might not be able to simplify tolerable versus intolerable noises based solely on volume. SPD is a matter of difficulty in processing information received through the senses  - though difficulties may arouse anxiety, "phobia" is a pretty specific irrational fear, not to be attributed to a difficulty in processing.
Specific phobia(s) and SPD aren't necessarily mutually exclusive, but one way in which they can be differentiated is by one of the symptoms for Specific Phobia.
C. The person recognizes that the fear is excessive or unreasonable. Note: In children, this feature may be absent. 
In SPD, what seems to be critical in response to stimuli is the idea of the "just-right" perception. In SPD, the reactive response to stimuli may not necessarily be indicative of a phobic response. For example, someone with SPD may absolutely hate being poked by others. But this person would not go out of his way to avoid being poked - dislike for tactile response purposes is different from a fear of pokes.