A square and a diamond
Three rhombi. Alternatively, a rhombus, and two irregular polygons with 5 or more sides, forur of which are equal. Apart from a rhombus there is no 4-sided shape that has equal sides but no right angles.
It isn't really a square if it has no equal sides. A trapezoid can be drawn that has no equal sides, some can have two sides equal. Quadrilaterals include those 4-sided shapes with no sides equal but they also include all other 4-sided shapes. You would need to specify "Quadrilateral with no equal sides".
rectangle
A rectangle has two pairs of equal sides. In other words, opposite sides of a rectangle are equal in length. This property distinguishes a rectangle from a square, which has all four sides equal in length.
a quadrilateral
The two quadrilaterals with equal sides are the rhombus and square.
I don't know if there's a specific name for these two shapes, but the only two shapes that have 4 equal sides are the square and rhombus. The difference between the two is the square has 4 equal angles (90 degrees) and a rhombus does not.
A rectangle has four sides with two equal lengths.
A shape with four or more sides can have two parallel sides.
Two different types of shapes would be a circle and a square. they differ from each other in the fact that a circle's shape is perpetual as a square has four equal sides and four corners.
Three rhombi. Alternatively, a rhombus, and two irregular polygons with 5 or more sides, forur of which are equal. Apart from a rhombus there is no 4-sided shape that has equal sides but no right angles.
square, diamond
A rectangle has two sets of two equal sides and four right angles.
It isn't really a square if it has no equal sides. A trapezoid can be drawn that has no equal sides, some can have two sides equal. Quadrilaterals include those 4-sided shapes with no sides equal but they also include all other 4-sided shapes. You would need to specify "Quadrilateral with no equal sides".
Squares and rectangles.
A rhombus is a shape having two acute angles and four equal sides.
Two shapes are similar when the sides of one are directly proportional to the corresponding sides of the other. That all the corresponding angles are equal.