This is based on browsing UCSD’s website and my own experience (I’m in an adjacent field) but not any direct experience with UCSD’s majors.
One important thing to note is that on the Department of Biological Sciences, it appears that the physiology and neuroscience major will no longer be offered to anyone entering after Fall 2017. The closest replacement seems to be neurobiology. Given that, I’m going to talk about the neurobiology major instead.
The neurobiology major is housed in the Department of Biological Sciences.
The major in cognitive science with a specialization in neuroscience is in the Department of Cognitive Science.
The major in cognitive and behavioral neuroscience is a joint major in the Department Cognitive Science and Psychology.
So, unsurprisingly, most of your upper-division major coursework in neurobiology is in the biological sciences - molecular biology, genetics, biochemistry, etc. It’s about learning about the biological structure and function of the nervous system.
In the CBN major, you’ll take roughly equal coursework in cognitive science and psychology. Cognitive behavioral neuroscience as a field is about linking the brain’s structure and function and neural activity with perception, basic psychological behaviors, and cognitive function. More simply put (at risk of oversimplifying), it’s about understand how your brain’s biological function drives your psychology.
In the cognitive science major with the neuroscience specialization, your upper-division coursework is primarily in cognitive science (which in and of itself is an interdisciplinary field combining psychology, linguistics, computer science, philosophy, and some other fields. At UCSD it is very old and well-established, though, and the classes are taught by dedicated faculty), but you also have the choice of taking courses in computer science, linguistics, psychology, and some other departments to round out your requirements.
Cognitive science is a more complex field interested in theory of mind, cognition and thought - ranging all the way from basic biological brain function to sensation and perception to how people and machines learn and remember things to people’s interaction with the sociocultural setting to ethics and philosophy and theory of mind.