No, but they are dependent on one another. A flexible employee is a worker who understands the mission of the company with passion, has priorities appropriately in place, invests time and effort into accomplishing their tasks to the best of their abilities, and does so consistently (even when life happens.)
A flexible workplace is a place of business that prioritizes the wellbeing of their employees and the quality of work above how and when the work gets done. It is a company that “emphasizes the willingness and ability to adapt to change.” (https://www.thebalancecareers.com/workplace-flexibility-definition-with-examples-2059699#:~:text=Flexible%20employees%2C%20for%20their%20part,do%20one%20or%20two%20tasks.)
You cannot have one successfully in place without the other. A flexible employee in a rigid workplace becomes an overworked and burnt-out workaholic, whereas a flexible workplace can become a company losing more money than it gains if its employees are too lax. If employees don’t have the mission in mind, priorities in place, grit to see things through, and regulation skills to press towards the company’s mission, they are not flexible and will drive a business into the ground.