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
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.
The two quadrilaterals with equal sides are the rhombus and square.
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.
A shape with four or more sides can have two parallel sides.
A rectangle has four sides with two equal lengths.
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 regular quadrilateral is a a four sided shape that has all of its sides equal in length. There are two shapes that satisfy these conditions, a square and a rhombus.
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.