A 4 sided polygon
square
quadrilateral
A quadrilateral.
A quadrilateral.
parallelogram
A square
Rectangle.
paralelagram or quadrilateral
quadrilateral
polygon, sometimes a parallelogram
I don't use the name "rhombus-quadrilateral", but perhaps the answer to your question is that a rhombus is a special kind of parallelogram
rhombus, quadrilateral.