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a rectangle, which has two sets of parallel side
Not necessarily. A quadrilateral is a plane shape with four straight sides. There is no requirement for a side to be parallel to another.
Any four-sided shape is a Quadrilateral. Square, Rectangle, Parallelogram, rhombus, trapezoid etc. It may have no parallel sides as in a kite, 1 parallel side as in trapezoid or 2 parallel sides as in parallelogram.
Strictly speaking you cannot have one parallel side - you must have one pair. Any irregular polygon with four or more sides can have a pair of parallel sides. Most have no specific names - the only one that does is a trapezium.
A trapezoid has 4 sides with one pair of opposite parallel sides of different lengths.