Rhombus and square.
* * * * *
No, they are not other names: they are names for two special kinds of parallelograms.
For example, if you have a dog called Rex, then Rex is not another name for dog - Rex is a name for your dog, and some others, but there are lots of dogs that are not Rex.
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Quadrilateral and parallelogram
square,
Quadrilateral and parallelogram
3 names for a parallelogram
Quadrilateral * * * * * Nonsense. Most quadrilaterals are not parallelograms.