Marine Biology is defined by the Scripps page as "the study of marine organisms, their development, and their adaptations. It is concerned with evolutionary, organismic, genetic, physiological, and biochemical processes in marine organisms, and the relationship between them and their biotic and physical environment."

So if you want a definition of a "Deep Sea Biology", you can substitute the term "deep sea" for "marine" in the above paragraph. The deep ocean is of interest to oceanographers of all stripes, because it is potentially important on a number of scales, from planetary (e.g. the global ocean conveyer belt, which is a pattern of circulation in the deep ocean over much of the planet; the sequestration of carbon from the atmosphere), to small scale (e.g. deep sea vents; microorganisms that live in the water and sediments).

Using my definitions, you could say that Biological Oceanographers are mostly interested in populations and the physical/chemical environment, while Marine (and Deep-Sea) biologists are interested in things like evolution, genetics, physiology and biochemistry. However, there's lots and lots of overlap, and Biological Oceanographers often use things like genetic markers, physiological rate measurements and biochemical markers in their work, and work to develop them. Overall, I'd say there's really not much difference!