Within the brain, a nucleus refers to a small region that contains the cell bodies of a group of associated neurons (as well as their supporting cells). Nuclei can be defined by their physical appearance; for example the substantia nigra (black substance) is named for it's dark appearance under a microscope, or for their function; for example the cochlear nuclei contain the presynaptic terminals of type I spiral ganglion neurons from the cochlea.
Typically, a nucleus contains:
Inputs: The axons of neurons that project from other brainstem nuclei.
Projecting neurons: That receive input at a dendritic tree within the nucleus and carry it along axons that project out of the nucleus.
Interneurons: That modulate the responses of projecting neurons.
Each nucleus may receive both excitatory and inhibitory inputs, as well as have both excitatory and inhibitory interneurons, allowing for complex processing of information while it travels along its pathway.
A Ganglion (pl. Ganglia) is a collection of the cell bodies of neurons outside of the central nervous system. Typically, both the dendrites and axons of neurons within a ganglion project outside the ganglion. For example the Dorsal Root Ganglia located near the spinal cord contain the cell bodies of sensory neurons, whose dendrites receive input from sensory receptors in the skin and axons project to synapses within the spinal cord.