Four coplanar line segments linked end to end to create a closed figure.
A 4-sided polygon.

Try this Drag the orange dots on each vertex
to reshape the quadrilateral.

The quadrilateral is any 4-sided polygon.
But it is the parent of a whole family of figures, each with their own distinct names and characteristics.
See also Tetragon.

Quadrangle

Quadrangle ("four angles") is another name for a quadrilateral.
However, it is a word often used for an open space where people gather, say on a school or university campus.
In this case the quadrangle (or "quad") is usually a rectangle or square.