Key Difference: A trapezium is a quadrilateral is that has at least one pair of parallel sides. The figure is more commonly known as a trapezoid. A parallelogram is a quadrilateral that has two pairs of parallel sides.
So a trapezium can be a parellelogram when both two pairs are parellel
but all trapeziums are not parellelogram
But every parellelogram can be a trapezium because always the two pairs of lines are in parellel
it satisfies the condition of trapezium