A state variable is one of the variables used to describe the state of a dynamical system. Each state variable corresponds to one of the coordinates of the underlying state space. An intuitive introduction tostate variables is given in the idea of a dynamical system.
A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system.