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>> All the four sides are congruent.

>> The opposite sides are congruent (not all the four sides)

I think that's the only difference about them. 

And we can conclude that square can be a rectangle but a rectangle could never be a square. ☺
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Their opposite side is parallel and congruent. Opposite angles are congruent. Consecutive angles are supplementary. However, in rectangle its diagonals bisect each other, congruent, and separate the parallelogram to 2 congruent angles. Whereas, square is perpendicular to its two diagonals.
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