The difference between Arc and Directed edge

Arc as a noun (astronomy):

That part of a circle which a heavenly body appears to pass through as it moves above and below the horizon.

Arc as a noun (geometry):

A continuous part of the circumference of a circle (circular arc) or of another curve.

Arc as a noun:

A curve, in general.

Arc as a noun:

A band contained within parallel curves, or something of that shape.

Arc as a noun (electrics):

A flow of current across an insulating medium; especially a hot, luminous discharge between either two electrodes or as lightning.

Arc as a noun:

A story arc.

Arc as a noun (mathematics):

A continuous mapping from a real interval (typically [0, 1]) into a space.

Arc as a noun (graph theory):

A directed edge.

Arc as a noun (basketball, slang):

The three-point line.

Arc as a verb (ambitransitive):

To move following a curved path.

Arc as a verb (transitive):

To shape into an arc; to hold in the form of an arc.

Arc as a verb (intransitive):

To form an electrical arc.

Directed edge as a noun (graph theory):

An edge of a directed graph.