Specific language impairment (SLI) and APD appear intertwined, with the suggestion that differential diagnosis may be influenced by whether a child is assessed by an audiologist or speech-language therapist. Multi-disciplinary assessment (as occurs at SoundSkills) is advisable.
Ferguson, M. A., Hall, R. L., Riley, A., & Moore, D. R. (2011). Communication, listening, cognitive and speech perception skills in children with auditory processing disorder (APD) or specific language impairment (SLI). Journal of Speech, Language, and Hearing Research.
https://pubs.asha.org/doi/abs/10.1044/1092-4388%282010/09-0167%29
Miller, C. A., & Wagstaff, D. A. (2011). Behavioral profiles associated with auditory processing disorder and specific language impairment. Journal of communication disorders, 44(6), 745-763.
https://www.sciencedirect.com/science/article/abs/pii/S0021992411000232