"Center" is a geometric term, while "middle" is a generic term.
ZV
EDIT:
cen·ter (sntr)
n.
A point or place that is equally distant from the sides or outer boundaries of something; the middle: the center of a stage.
A point equidistant from the vertices of a regular polygon.
A point equidistant from all points on the circumference of a circle or on the surface of a sphere.
A point around which something rotates or revolves: The sun is the center of our solar system.
A part of an object that is surrounded by the rest; a core: chocolates with soft centers.
A place where a particular activity or service is concentrated: a medical center.
A point of origin, as of influence, ideas, or actions: a center of power; a center of unrest.
An area of dense population: a metropolitan center.
A person or thing that is the chief object of attention, interest, activity, or emotion.
A person, object, or group occupying a middle position.
often Center A political group or a set of policies representing a moderate view between those of the right and the left.
Physiology. A group of neurons in the central nervous system that control a particular function: the vasomotor center.
Sports. A player who holds a middle position on the field, court, or forward line in some team sports, such as football and basketball.
Baseball. Center field.
A small conical hole made in a piece of work with a center punch so that a drill can be accurately positioned within it.
A bar with a conical point used to support work, as during turning on a lathe.
Architecture. A centering.
mid·dle (mdl)
adj.
Equally distant from extremes or limits; central: the middle point on a line.
Being at neither one extreme nor the other; intermediate.
Intervening between an earlier and a later period of time; being an intermediate part of a sequence or series: the middle years.
Middle Geology. Of or relating to a division of geologic time between an earlier and a later division: the Middle Paleozoic.
Middle Of or relating to a stage in the development of a language or literature between earlier and later stages: Middle Swedish.
Grammar. Of, relating to, or being a verb form or voice in which the subject both performs and is affected by the action specified.
n.
An area or a point equidistant between extremes; a center: the middle of a circle.
Something intermediate between extremes; a mean.
The interior portion: the middle of a chain.
The middle part of the human body; the waist.
Logic. A middle term.
Grammar.
The middle voice.
A verb form in the middle voice.
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