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Any shape wit four of more sides can have one pair of parallel sides.
Any polygon with four or more sides can have a pair of parallel sides. It is also possible to to have non-polygonal shapes - eg a cigar-shape - that has parallel sides.
A trapezoid has exactly one pair of parallel sides
A parallelogram is an quadrilateral (a figure with four edges and four vertices) with two sets of parallel sides. A trapezoid, also known as a trapezium, is a shape with four sides with a pair of parallel sides.
Any shape with four straight sides is a quadrilateral. A trapezoid has one pair of parallel sides, and a parallelogram has two pairs of parallel sides. So any shape with four straight sides and no parallel sides is a quadrilateral that is not a parallelogram or trapezoid.