Not much, other than they both can be parts of a 3-dimensional figure.
"Vertices" is plural of "vertex", which is a point. The vertex of an angle, for example, is the point of intersection between two lines. 2-dimensional and 3-dimensional figures can have vertices.
An "edge", however, is a line segment, and only 3-dimensional figures (cubes, pyramids, etc) can have edges. An edge is the intersection of two sides of a figure.
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No. Edges join vertices; or, put another way, edges meet at vertices.
Four or more place polygonal faces. Four or more vertices. Six or more edges. Faces + Vertices = Edges + 2
A trapezium has 4 edges and 4 vertices.
8 vertices and 12 edges.
Vertices : 8 Edges : 12