Neither the managing director nor the CEO is higher than the other, because both of these terms refer to similar positions. American companies use the title CEO, or chief executive officer, while British English often uses the term "managing director."
Whichever term is used, the people who fill these jobs generally report to the company's board of directors. Because of the differences between American and British corporate law, there are some slight differences in the job descriptions. For example, an American CEO is only responsible for his company's success, but according to Britain's Companies Act 2006, managing directors are expected to consider the societal and environmental impact of their decisions.