Brain centers vs areas (and how they relate to nuclei)

I’m looking for a reputable source that can provide succinct definitions differentiating the following terms in the central nervous system (CNS; particularly in the brain):

• Area

• Center

• Nucleus

Examples include Wernicke’s area, piriform area, deglutition center, olivary nuclei, vestibular nuclei, etc.

Really, I’m trying to corroborate my experiences having seen many examples of each but never having seen official definitions of either centers or areas. I know well that a nucleus is a cluster of cell bodies in the CNS [ex: source]. I also feel as though areas are regions with functionally-related roles, and that they tend to be associated with the cerebral cortex. Centers seem to be deeper functional regions.

What I’m not clear on is what the official differences between an area and a center are, whether (or to what degree) either term is inclusive vs exclusive of nuclei, and to what degree the relationship of all three words overlap either structurally or functionally.

• I do know that Tortora & Derrickson (15th ed, 2017) indicate explicitly that certain centers are nuclei, but I’m not sure whether this more broadly describes all centers or is simply indicates a narrow example of a center.

Examples of nuclei in the medulla …include the cardiovascular center and medullary rhythmicity center.

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^{Motivation: trying to find a reputable source to provide a simple definition for my students. I usually just run with broad explanations based on repeated exposure of each, but I think my students would appreciate a cited, specific definition of each term.}