What is the difference between Neuroscience and Neurobiology?

Answer 1

Neurobiology:
is the study of cells of the nervous system and the organization of these cells into functional circuits that process information and mediate behavior.It is a subdiscipline of both biology and neuroscience.

Neuroscience:
Neuroscience is a field of study which deals with the structure, function, development, genetics, biochemistry, physiology, pharmacology and pathology of the nervous system.

Answer 2

Neuroscience studies everything having to do with nerve cells and nervous tissue in any way. Thus it can include biology, anatomy, psychology, statistics, surgery, pharmacology, and quite a few other fields. Just so long as they're working on something relevent to nervous stuff.

Neurobiology is a SUBFIELD. It studies only the cells themselves as cells. I suppose you might think of it as the area where neuroscience and biology overlap, though again it is mostly focused on neurons and glial cells instead of even other aspects of biology.