They can be, but whether they should depends on the circumstances. It is common for individuals to nominate the same person to serve as both executor of their will and trustee of their trust, particularly when they have confidence in a trusted family member or friend.
Appointing the same individual to both roles can simplify estate administration by providing continuity, reducing the need for coordination between multiple fiduciaries, and, in some cases, lowering administrative costs. However, it may also have drawbacks. For example, concentrating both roles in a single person can increase the potential for family conflict or reduce an important layer of oversight that may exist when different individuals serve as executor and trustee.
Ultimately, the decision should be based on the will and trust creator’s goals, the complexity of the estate, and the qualifications and trustworthiness of the individuals being considered.