edge vs boundary

edge and boundary both are nouns.

Word	Noun	Adjective	Verb	Adverb
edge	Yes	No	Yes	No
boundary	Yes	No	No	No

As nouns, boundary is a hypernym of edge; that is, boundary is a word with a broader meaning than edge:

Other hypernyms of edge include bound, bounds.

As nouns, edge and boundary are synonyms defined as:

Other synonyms of edge include bound.

edge (noun)	boundary (noun)
a sharp side formed by the intersection of two surfaces of an object	the greatest possible degree of something
the outside limit of an object or area or surface; a place farthest away from the center of something	the line or plane indicating the limit or extent of something
a slight competitive advantage	a line determining the limits of an area
the attribute of urgency in tone of voice
the boundary of a surface
a line determining the limits of an area

edge (verb)	boundary (verb)
lie adjacent to another or share a boundary
provide with an edge
advance slowly, as if by inches
provide with a border or edge