A quadrilateral is a polygon that has four sides, four corners (or vertices), and four angles. It is a broad category that includes various shapes such as squares, rectangles, trapezoids, and rhombuses.
On the other hand, a parallelogram is a specific type of quadrilateral that has opposite sides that are both equal in length and parallel. This means that a parallelogram not only possesses the properties of a quadrilateral but also has additional characteristics, such as opposite angles being equal and adjacent angles being supplementary.
In summary, while all parallelograms are quadrilaterals, not all quadrilaterals are parallelograms. The distinguishing factor lies in the properties of the sides and angles. A rectangle and a square are examples of parallelograms, but a trapezoid, with only one pair of parallel sides, is an example of a quadrilateral that is not a parallelogram.