Recently I have discovered that I have a Substance Abuse disorder, also known as, addiction. However, I have a history of depression as well, is there a term for that?

Yes, actually there a few different terms that refer to experiencing not only an addiction but a mental health disorder as well. The most common terms used to identify this subject are: Comorbidity and Dual-diagnosis. Having multiple mental health disorder diagnosis’s is considered to be Dual-diagnosed and Comorbidity.