In transitive terms the difference between fight and square
is that
fight is to try to overpower; to fiercely counteract while
square is to draw, with a pair of compasses and a straightedge only, a square with the same area as.
In archaic terms the difference between fight and square
is that
fight is a battle between opposing armies while
square is to take opposing sides; to quarrel.
In obsolete terms the difference between fight and square
is that
fight is a screen for the combatants in ships while
square is to go to opposite sides; to take an attitude of offense or defense, or of defiance; to quarrel.
As verbs the difference between fight and square
is that
fight is to contend in physical conflict, either singly or in war, battle etc while
square is to adjust so as to align with or place at a right angle to something else.
As nouns the difference between fight and square
is that
fight is an occasion of fighting while
square is a polygon with four sides of equal length and four angles of 90 degrees; a regular quadrilateral whose angles are all 90 degrees.
As an adjective square is
shaped like a square (the polygon).