A rectangle is a parallelogram whose sides intersect at 90° angles. Now, since a rectangle is a parallelogram, its opposite sides must be congruent.
A square is also a parallelogram whose sides intersect at 90° angles. Therefore, like a rectangle its opposite sides are congruent. However, a square has an added feature. It is also a rhombus. Therefore, all of its sides are congruent.
A rectangle is a square when both pairs of opposite sides are the same length. This means that a square is a specialized case of the rectangle and is indeed a rectangle.
What extra properties does the square have?
Well, the only difference is that a square is also a rhombus so the square has all the properties of a rhombs while a rectangle does not.