Every square is a rectangle, but not every rectangle is a square. A rectangle always has 4 right angles. So does a square, so that can be considered a rectangle. A rectangle can have sides of any length just as long as all four angles are right angles. A square however must have congruent sides. So not all rectangles are squares, only the rectangles with 4 congruent sides. In real life imagine that you are ordering flowers and you want tulips. A tulip is considered a flower, but are all flowers considered tulips?
A rectangle can be considered a parallelogram with 4 right angles. A rhombus is a parallelogram with 4 congruent sides. A square is a rhombus with 4 right angles. It is almost like having 3 people in a car, but 2 people are mothers and 2 are daughters. This is possible because in the car there is a woman, her daughter, and her daughter's daughter.
Daughters can also be mothers.
Is it possible to have a rectangle that is not a square? Yes.
Is it possible to have a parallelogram that is not a rectangle? Yes, a rectangle has 4 right angles and all sides are parallel. however a parallelogram can not be considered a rectangle because it does not have 4 right angles even though the lines are all parallel.
Is it possible to have a rectangle that is not a parallelogram? No, All rectangles are parallelograms, because the sides in a rectangle are always parallel.