A quadrilateral with one pair of parallel sides is a trapezoid.
If it has two pairs of parallel sides it is a parallelogram, but parallelograms are also trapezoids in the same way that dogs are also mammals.
A parallelogram has two pairs of congruent sides. (They may all be congruent, in which case it is a rhombus, but a rhombus is also a parallelogram in the same way that a poodle is also a dog). Therefore the shape you describe is not a parallelogram.