What term describes an individual employed under contract and control of an employer?

The correct term that describes an individual employed under a contract and under the control of an employer is "employee." An employee is someone who works for an organization or individual and is subject to the employer's directives and oversight regarding the completion of their tasks. This relationship is typically characterized by a formal agreement outlining the terms and conditions of employment, including duties, compensation, and the nature of control the employer has over the employee's work.

In contrast, a contractor usually works independently and has more autonomy over how they complete their tasks, which differentiates them from employees. A supervisor is a role focused on overseeing employees or operations but does not inherently define the relationship between an employer and an individual worker. Similarly, a manager holds a leadership position typically involving overseeing employees and making organizational decisions, but again does not specify the employment relationship itself. Therefore, "employee" is the most accurate term for describing the relationship defined in the question.