Difference between Parallelogram and Quadrilateral
Students of primary classes often mix many geometrical terms with each other because of the similarities in them. Parallelogram and quadrilateral are the terms which are frequently misunderstood by the students who start to learn the Euclidean geometry.
Just keep in mind that a quadrilateral is a polygon which has four sides. On the other hand, a parallelogram is a quadrilateral which has two pairs of the parallel sides which make it different from other quadrilaterals like square and rectangle. Furthermore, the opposite angles and sides of the parallelogram are equal.
Instructions

1
Parallelogram
It is a simple i.e. non selfintersecting type of a quadrilateral which has two pairs of parallel sides each. The opposite sides of the parallelogram have equal lengths and the opposite angles have equal measurement. Furthermore, you must know that the congruence of the opposite angles and sides of the parallelogram is always in direct effect of the Euclidean Parallel Postulate, a condition which cannot be proven without taking help from that postulate. In addition, it will be important to note that the threedimensional equivalent of any parallelogram is called as parallelepiped.
The diagonals of a parallelogram bisect with each other. Moreover, one pair of the opposite sides of a parallelogram is always equal in length. The adjacent angels of a parallelogram are always supplementary and two congruent triangles are formed if you divide each diagonal of the parallelogram. It will be interesting to note that the sum of squares of all the sides is equal to the sum of square of all the diagonals in the parallelogram (this is called as Parallelogram Law). Besides, the parallelogram has a rotational symmetry of ‘order two’.
Furthermore, the area of a parallelogram is two times the area of a triangle which is created by one of the diagonals in it. Additionally, the area of a parallelogram is always equal to the scale of the cross product of vector of the two adjacent sides. If you draw a line from the midpoint of a parallelogram, it will bisect its area.

2
Quadrilateral
It can simply be defined as a polygon which has 4 sides or corners (4 vertices or edges). It is sometimes used as an analogy with the triangle which has three edges, with tetragon for the consistency, with pentagon which as 5 sides and hexagon which has 6 sides.
The simple quadrilaterals can either be convex or concave. The sum of interior angles of a quadrilateral is 360.