Shapes with 4 sides are called quadrilaterals. If all the sides of the shape have the same length, then there are two options for specific quadrilaterals. These are squares or rhombuses. If the pairs of sides are not the same length as each other, then there are two alternate options for the shape. These are rectangles and parallelograms.
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This is called a Parallelogram. Each pair of opposite sides will then be the same length. If all four sides are the same length, and opposite sides are parallel, then it is a rhombus. NB: If all four sides are the same length then the opposite sides must be parallel.
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A regular polygon requires all sides to be the same length; in a rectangle not all four sides are the same length (they form two pairs of sides of equal length) and so it is not a regular polygon.
I am not sure if you are saying that the opposite sides are the same length, if so you just have a parallelogram. If you are asking for all four sides to be the same length, you have a rhombus. If the angles are right angles, you have a square. ■
No shape has four equal sides and four different angles - either there are two pairs of equal angles, or all four angles are the same; or all sides are not the same length.