I'm going to put DSH next time a questionnaire asks about my race
I always took Domestic x Hair to be anything that wasn't a particular breed. If it's not Siamese, Burmese, Bengal etc. it's just a run of the mill housecat, and it has short hair it's a DSH, medium hair DMH, long hair, DLH.
Like has been said, it's so people can put a breed into the box