The description of British organizations may be correct, but this description of U.S. organizations is not. The correct version is:...
A typical company has a Board of Directors.
The Board has a President.
The Board employs a Chief Executive Officer.
If it wishes, the Board may actually employ the President as CEO; he is then President and Chief Executive Officer.
There are many different types of company with many variations on these structures.
Non-commercial organisations will use CEO rather than MD.