Yes any square is also a parallelogram, but not the other way around (some parallelograms are not squares). In other words, any square is a parallelogram.
If you draw a Venn Diagram, the set of squares will be entirely inside the set of parallelograms.
This is because any rhombus is also a parallelogram, and the same applies to rectangles as well. A square is the combination of a rhombus and rectangle.
Rhombus = four sided figure where all sides are equal
Rectangle = four sided figure where all angles are equal to 90 degrees