The difference between Apex and Vertex

Apex as a noun:

The "highest" or the greatest point of something.

Apex as a noun (figuratively):

The moment of greatest success, expansion, etc.

Apex as a noun (geometry):

The topmost vertex of a cone or pyramid (in their conventional orientation).

Apex as a noun (chiefly, anatomy):

The "pointed" fine end of something. The lowest part of the human heart. The deepest part of a tooth's root.

Apex as a noun (botany):

The end of a leaf, petal or similar organ opposed to the end where it is attached to its support; the tip.

Apex as a noun (astronomy):

The point on the celestial sphere toward which the sun appears to move relative to nearby stars.

Apex as a noun (physics):

The lowest point on a pendant drop of a liquid.

Apex as a noun (mining, US):

The end or edge of a vein nearest the surface.

Apex as a noun (typography):

A diacritic in Classical Latin that resembles and gave rise to the acute.

Apex as a noun (typography):

A diacritic in Middle Vietnamese that indicates .

Vertex as a noun:

The highest point of something.

Vertex as a noun (anatomy):

The highest surface on the skull.

Vertex as a noun (geometry):

The common point of the two rays of the angle, or its equivalent structure in polyhedra (meeting of edges) and higher order polytopes.

Vertex as a noun (mathematics):

A point on the curve with a local minimum or maximum of curvature.

Vertex as a noun (graph theory):

One of the elements of a graph joined or not by edges to other vertices.

Vertex as a noun (computer graphics):

A point in 3D space, usually given in terms of its Cartesian coordinates.

Vertex as a noun (optics):

The point where the surface of a lens crosses the optical axis.

Vertex as a noun (nuclear, or, particle physics):

An interaction point.

Vertex as a noun (astrology):

The point where the prime vertical meets the ecliptic in the western hemisphere of a natal chart.