Center, middle, midst, core, hub, focus, nucleus, heart are comparable when meaning the point, spot, or portion of a thing which is comparable to a point around which a circle is described.
Center approximates more or less closely its strict geometrical sense as the point within a circle or sphere that is equidistant from every other point on the circumference or is the average distance from the exterior points of a body or figure.
Center may be extended to a thing or a part of a thing wKich suggests a geometrical center especially in being the point around which the rest rotates or revolves or at which all lines (as of activity) converge or from which every line, or branch radiates or which lies midway between extremes.
Middle is less precise than center and suggests a space rather than a point; it is the part of an object which includes and surrounds the center; thus, the middle of a room is the central portion of it.
Middle, unlike center, also applies to what has duration and to merely linear extension. Middle may be applied freely to something which lies between the beginning and end (as of a process, a course, or a piece of work).
Midst is often used in place of middle for a point or spot well within a group or number of enveloping persons or objects or of things (as duties, affairs, and burdens) that surround or beset one; however it seldom occurs except in a prepositional phrase introduced by in, into, from, out of.
Core basically denotes the central portion of certain fruits (as the apple) which is made up of papery or leathery envelopes containing seeds and is often extended to something that similarly lies at the center of a thing and that resembles an apple core in being unconsumed or unused or in forming a firm central mass in a growth or in having a different character from that which surrounds or encloses it or often in being the very center of a thing's life, significance, or power.
Hub, which primarily denotes the central and usually solid part of a wheel from which the spokes radiate and which rotates on (or with) the axle, is often extended to a place, person, or thing on which other places, persons, or things depend for their life, activity, ideas, or progress.
Focus is applicable to a point of convergence or concentration or, sometimes, in nontechnical use, of emanation; thus, the point at which rays of light meet after reflection or refraction is called a focus; a person to whom all eyes are turned is the focus of attention.
Nucleus applies especially to a vital and usually small and stable center about which matter is gathered or concentrated or to which accretions are made.
Heart applies to a place or thing that lies well within something (as a region or system) and which determines the essential character of the whole or serves as a vital, positive, or motivating part.