Neuroscience is the catchall phrase for the various neural sciences. A Neural Science is a science that studies The Nervous System. There are a lot of Neuro-Sciences, including Neuropsychology, Neurobiology,Neurochemistry, Molecular Neuroscience, CellularNeuroscience, etc. The Neuro Sciences are all fairly young in the terms of science, if only because the Nerve was only discovered in the 1900's. What has made this field interesting in the last 20 years is the growth of technology capable of looking into the nature of the neuron, and how it connects together to form larger units like the brain.
When evaluating theories in Neuroscience we must accept that much of what we know will change over time, and that the nature of the images we get about the brain are not yet good enough to capture the whole operation of the brain at the neural level.
Phenomenal Consciousness, and especially the work of Dr. Edelman are partly supported by the Neuro Sciences Institute (NSI) which was started by Dr. Edelman as a technolgical monastery to support research into Neuroscience. As a result, the Phenomenal Consciousness School is closer to Neuroscientific thought.
For a more detailed overview, see the Fundamentals of Neuroscience course.