A quadrilateral has four sides, and the fact that it is equilateral means the sides all have the same length, so the only possible shapes with four sides of equal length are a square and a rhombus.
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No, a square is an equilateral quadrilateral. http://en.wikipedia.org/wiki/Quadrilateral
Rectangle
A square is a rectangle, a rhombus, an equilateral parallelogram, and a regular quadrilateral.
A rhombus is any equilateral ( all four sides congruent) quadrilateral. If it has right angle for the vertices then it is a rectangle called a square.
You could call it a regular quadrilateral, or an equilateral rectangle or even an equiangular rhombus, if you prefer.