What is the difference between a parallelogram and a trapizoid

A parallelogram is a figure with 4 straight sides whose opposite sides are parallel and equal in length and whose opposite angles are equal. a trapezoid is also a figure with 4 straight sides however, only one pair of opposite sides is parallel.  

Well, a parallelogram is a 4-sided flat shape with straight sides where opposite sides are parallel.
Also:
• opposite sides are equal in length, and
• opposite angles are equal
And a trapizoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel.

So the difference between a trapizoid and a parallelogram is very simple:
A trapezoid has exactly one pair of parallel sides and a parallelogram
has exactly two pairs of parallel sides.