Just because a 4 sided object has equal length does not mean it has equal angles of 90 degrees each. Think of 2 equilateral triangles placed next to each other.

The sides would all be equal, but the angles would be 60,60,120,120

Also, worth pointing out that the area of a square is s^2, but the area of a rhombus is the same as that of a parallelogram, base*height.

Think of a rhombus as a slanted square. A square is a solid box, but a rhombus's joints can be bent, which is why the angles don't have to be equal. But the angles all add up to the same amount as the angles in a square, the perimeter is the same as a square. Also, the angles opposite each other have to be equal. Two of the angles in a rhombus are equal, and then the other two are also equal to each other.

Also, think of it in terms of categories. The bigger category is parallelograms. Within that category lies the rhombus. Among rhombuses, those with right angles are called squares.