Its a rhombus,( it's so of a tilted square looks like a parallelogram only that with this shape all sides are equal.
A trapezoid is quadrangle (or quadrilateral) with one set of parallel sides. Many mathematicians define a trapezoid to have only one set of parallel sides, which specifically excludes parallelograms. Using this definition, an isosceles trapezoid is a quadrangle that has two sides that are equal, but is not a parallelogram. I suspect this the answer to your question; however, I should note that most mathematicians allow one or both sets of sides to be parallel. Using the latter definition, the isosceles trapezoid is not always, but it could be a parallelogram (similar to the way a rectangle is not always, but could be a square).
Isosceles trapezoid may be the same, but not always