Such a shape is called a rhombus.
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You don't tell us enough information. In a square, there are four sides and four angles. The sides are all equal and the angles are all right angles. In a rectangle, there are four sides and four angles The opposite sides are equal and the angles are all right angles. There is no other shape in which all angles are right angles.
A four sided figure with four equal sides and no right angles is a diamond, or a rhombus. If it had four right angles, it would be a square.
Four equal sides and four right angles is the definition of a square.
A rhombus has four equal sides but no right angles.
A figure with four equal sides and no right angles is a rhombus. A rhombus is comprised of two acute angles and two obtuse angles.