A parallelogram is a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse trapezoids or right trapezoids (rectangles). A tangential trapezoid is a trapezoid that has an incircle.
Both are quadrilaterals. A trapezoid has one pair of parallel sides, whereas a parallelogram has two pairs of parallel sides. Nothing is specified about the other two sides do a trapezoid. It is possible that this pair is also parallel, in which case the shape is also a parallelogram.
