Are degenerative disc disease and disc space narrowing two terms for the same disease?

YES: Degenerative disk "disease" is a misnomer. This is not a disease but rather describes the normal age related processes that occur to our disks. These changes include disk dehydration, disk bulging / protrosions/ herniations, and disk space narrowing. These processes can be visualized nicely with an MRI scan and sometimes can be inferred by an xray.

Not exactly: Degenerative disc disease is a broad term and can mean that the disc has become desiccated (losing water content) and appear black on a t2 weighted MRI sequence. As this progresses the height of the disc can be lost (disc narrowing). So to sum it up not all degenerative discs have narrowing of height but all narrowed discs are degenerated. Hope this helps!