Edge vs. Border

Border
Borders are geographic boundaries of political entities or legal jurisdictions, such as governments, sovereign states, federated states, and other subnational entities. Borders are established through agreements between political or social entities that control those areas; the creation of these agreements is called boundary delimitation.
Some borders—such as a state’s internal administrative border, or inter-state borders within the Schengen Area—are often open and completely unguarded. Other borders are partially or fully controlled, and may be crossed legally only at designated border checkpoints and border zones may be controlled.
Borders may even foster the setting up of buffer zones. A difference has also been established in academic scholarship between border and frontier, the latter denoting a state of mind rather than state boundaries.

Wikipedia

Edge (noun)
The boundary line of a surface.
Edge (noun)
A vertices of a polygon; the place where two faces of a polyhedron meet.
Edge (noun)
An advantage.
“I have the edge on him.”
Edge (noun)
The thin cutting side of the blade of an instrument, such as an ax, knife, sword, or scythe; that which cuts as an edge does, or wounds deeply, etc.
Edge (noun)
A sharp terminating border; a margin; a brink; an extreme verge.
“The cup is right on the edge of the table.”
“He is standing on the edge of a precipice.”
Edge (noun)
Sharpness; readiness or fitness to cut; keenness; intenseness of desire.
Edge (noun)
The border or part adjacent to the line of division; the beginning or early part (of a period of time)
“in the edge of evening”
Edge (noun)
A shot where the ball comes off the edge of the bat, often unintentionally.
Edge (noun)
A connected pair of vertices in a graph.
Edge (noun)
In male masturbation, a level of sexual arousal that is maintained just short of reaching the point of inevitability, or climax; see also edging.
Edge (verb)
To move an object slowly and carefully in a particular direction.
“He edged the book across the table.”
Edge (verb)
To move slowly and carefully in a particular direction.
“He edged away from her.”
Edge (verb)
To win by a small margin.
Edge (verb)
To hit the ball with an edge of the bat, causing a fine deflection.
Edge (verb)
To trim the margin of a lawn where the grass meets the sidewalk, usually with an electric or gas-powered lawn edger.
Edge (verb)
To furnish with an edge; to construct an edging.
Edge (verb)
To furnish with an edge, as a tool or weapon; to sharpen.
Edge (verb)
To make sharp or keen; to incite; to exasperate; to goad; to urge or egg on.
Edge (verb)
To delay one’s orgasm so as to remain almost at the point of orgasm.

Border (noun)
The outer edge of something.
“the borders of the garden”
Border (noun)
A decorative strip around the edge of something.
“There’s a nice frilly border around the picture frame.”
“a solid border around a table of figures”
Border (noun)
A strip of ground in which ornamental plants are grown.
Border (noun)
The line or frontier area separating political or geographical regions.
“The border between Canada and USA is the longest in the world.”
Border (noun)
Short form of border morris or border dancing; a vigorous style of traditional English dance originating from villages along the border between England and Wales, performed by a team of dancers usually with their faces disguised with black makeup.
Border (verb)
To put a border on something.
Border (verb)
To form a border around; to bound.
Border (verb)
To lie on, or adjacent to, a border of.
“Denmark borders Germany to the south.”
Border (verb)
To touch at a border (with on or upon).
“Connecticut borders on Massachusetts.”
Border (verb)
To approach; to come near to; to verge (with on or upon).

Wiktionary

Edge (noun)
the outside limit of an object, area, or surface
“she perched on the edge of a desk”
“a willow tree at the water’s edge”
Edge (noun)
an area next to a steep drop
“the cliff edge”
Edge (noun)
the point immediately before something unpleasant or momentous occurs
“the economy was teetering on the edge of recession”
Edge (noun)
the sharpened side of the blade of a cutting implement or weapon
“a knife with a razor-sharp edge”
Edge (noun)
the line along which two surfaces of a solid meet.
Edge (noun)
an intense, sharp, or striking quality
“a flamenco singer brings a primitive edge to the music”
“there was an edge of menace in his voice”
Edge (noun)
a quality or factor which gives superiority over close rivals
“his cars have the edge over his rivals'”
Edge (verb)
provide with a border or edge
“the pool is edged with paving”
Edge (verb)
move or cause to move gradually or furtively in a particular direction
“Hazel quietly edged him away from the others”
“she tried to edge away from him”
Edge (verb)
give an intense or sharp quality to
“the bitterness that edged her voice”
Edge (verb)
strike (the ball) with the edge of the bat; strike a ball delivered by (the bowler) with the edge of the bat
“Haynes edged to slip”
“he edged a ball into his pad”
Edge (verb)
ski with one’s weight on the edges of one’s skis
“you will be edging early, controlling a parallel turn”

Oxford Dictionary

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