Well, no sketches here.
1) A parallelogram has two sets of parallel sides. A trapezium does not.
2) A rhombus is a quadrilateral with 4 congruent sides (i.e., they all have the same length). A square is a special rhombus (so it has 4 congruent sides) in which every angle is a right angle (i.e., measures 90 degrees).
That's as succinct as it gets, I suppose.