A quadrilateral is a shape with four sides. A parallelogram is a quadrilateral that has two pairs of parallel sides (i.e. the sides opposite each other are parallel). A rectangle, for example, is a parallelogram. A trapezoid, however, is an example of a quadrilateral that is not a parallelogram - it has four sides, but only two of them are parallel to each other.
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An octagon is neither a quadrilateral nor a parallelogram. "Quadrilateral" refers to a shape that has four sides. "Parallelogram" refers to a shape that has two pairs of opposite, congruent sides. An octagon has eight sides, and since eight is not equal to four, an octagon is neither a quadrilateral nor a parallelogram.
A quadrilateral. It may be a rectangle, parallelogram, trapezoid, or an irregular quadrilateral.
A parallelogram must have 4 sides and so it must be a quadrilateral. However, the sides of a quadrilateral need not be parallel so a quadrilateral need not be a parallelogram.
It can be a square or a even a parallelogram! It's just something with 4 sides.
A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral in which the opposite sides are parallel.