In this title, “contractual employee” means an individual: who, under a written agreement, provides temporary personal services to the State for pay; who is not employed in a budgeted position; and who has an employer-employee relationship with the State in which the State: furnishes necessary tools and a place to work; has the right to control and direct the details, means, and results of the performance of the services; and has the right to discharge the individual from employment. “Contractual employee” does not include an individual who is employed as: an employee in the: skilled service; professional service; management service; or executive service; or an emergency employee.