No, but they are the most senior employee/operational position in the firm.
A Chief Executive Officer is a specific corporate title that is applied to a principal of a corporation, specifically the chair/head of a board, so the use of that title implies that a corporate board exists as well as stockholders, etc.
A managing director is less specific. The term 'director' can be used as a title for a company principal or owner, and can be applied to someone on the board, etc. However, that title can also be applied to someone who is strictly an employee. In larger companies, you'll see titles like 'Director of Online Marketing' and those people are frequently NOT actual principals, stockholders, or directors of the corporation - they are employees. The term 'managing director' typically refers to a top-level employee who liaises between the board OR is part of the board but also has day-to-day duties.
This term is also widely used for small/individual companies where a single person is holding all titles from the principals to the employees, and they need a title. For that purpose, it's quite accurate because that person is technically a 'director' (principal) of the company and is an employee who is managing day-to-day affairs.
CEO and managing director, Woolworths
Mr.Tarunshivam is now the ceo and managing director of Portweb Inc. world wide.
N.R.K Raman, CEO & Managing Director, i-flex solutions Ltd
Mr Shinzo Nakanishi is Managing Director and CEO of Maruti Suzuki
There is not an overall manager, this is a Managing Director and a CEO
Mr Ravi Narain Managing Director & CEO National Stock Exchange
Mr. Sanjeev Aga, Managing Director
The Managing Director of MRF Tyres is Arun Mammen.
Shri.sk.chakrabarti is the managing director(md) of axis bank and ceo of axis bank.dr.r.h.patil is the deputy managing director (dmd)