General term for a polygon with 4 sides is a quadrilateral. A parallelogram is the special case with two pairs of parallel sides.
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parallelogram
A square is a four-sided polygon with two congruent parallel sides.
A four-sided polygon with opposite sides parallel and all sides congruent is a square.
A square or a rhombus
That depends somewhat on other characteristics of the polygon.-- If it has four sides and one pair of them is parallel and congruent, then theother pair must also be parallel and congruent, and it's called a parallelogram.-- If it has four sides, parallel and congruent opposite sides, and a right angle,then it's called a rectangle.-- If it has four sides and all four sides are congruent, then opposite sides must beparallel, and it's called a rhombus.-- If it has four sides and both pairs of sides are parallel and all four are congruentand it has a right angle, then it's called a square as well as a rhombus.-- Any polygon with more than four sides can have at least one pair of oppositeparallel congruent sides and possibly more, but doesn't necessarily have.-- If it's a regular polygon, then it has one or more such pairs of sides if, and only if,it has an even number of sides.-- In any case with more than four sides, the polygon is named for its number of sides.And I believe that pretty well covers it.