A kite can be both a rhombus and a square.
A kite is a quadrilateral (four sided shape) where the four sides can be grouped into two pairs of adjacent (next to/connected) sides that are equal length.
So, if all sides are equal, we have a rhombus. If all sides are equal, and all angles of the quadrilateral are equal, then we have a square.
A square is a rhombus is a kite is a quadrilateral.
A kite is not always a rhombus. A rhombus is not always a square.