Which category of hackers includes those who operate in both ethical and unethical manners?

The category of hackers that includes those who operate in both ethical and unethical manners is the gray hats. Gray hat hackers often find themselves in a moral gray area; they might exploit vulnerabilities in systems without permission but do so with the intent of alerting the organization about the security issue rather than malicious intent. This duality in their actions distinguishes gray hats from other hacker categories.

Black hat hackers engage in unethical activities, typically for personal gain or to cause harm, while white hats are strictly ethical hackers who seek to protect systems and improve security. Elite hackers refer to highly skilled individuals in the domain but do not specifically denote ethical or unethical behavior. Thus, gray hat hackers occupy a unique position where their actions can straddle both ethical and unethical lines, making them the correct answer in this scenario.