Rhombus has 4 equal sides and no right angles
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 square. Its opposite sides are equal and it has 4 right angles.
it has 4 equal sides and no right angles
It's impossible for a quadrilateral to have no equal sides and have right angles.
A rhombus has four equal sides but no right angles.
A quadrilateral with four equal sides but no right angles is a rhombus.
Rectangle
A parallelogram with four equal sides and no right angles is a rhombus.
A square has 4 equal sides with 4 right angles.
It is a square that has 4 equal sides and 4 right angles.
The shape you are looking for is a quadrilateral. If you have a square, all angles MUST be right angles. A parallelogram can also have 4 equal sides in length and parallel sides, but a parallelogram doesn't have right angles.