You seem to worry a lot about things that need not be worried for. If you are starting a business with another person, instead of self-proclaiming business titles like those, keep it simple. If you plan on partnering together and doing an equal share of the work, you are both the "boss." If not, and one is putting more effort in than the other, then the one doing less will be inferior, and the titles really should not matter. And another route to go about it, if you are running some business that has more than one branch to work off, you would be the boss of one branch and they would be the boss of the other.
I was talking in reference to a huge corporation. Someone asked me the order and ranks of an organisation and I was tongue tied so I thought I should ask. Learning never hurts, does it? Though I thank you for your reply.
From wikipedia (not so trustable source, but a source none-the-less!)
"Typically, a CEO has several subordinate executives, each of whom has specific functional responsibilities. Common associates include a chief business development officer (CBDO), chief financial officer (CFO), chief operating officer (COO), chief marketing officer (CMO), chief information officer (CIO), chief communications officer (CCO), chief legal officer (CLO), chief technical officer (CTO), chief creative officer (CCO), chief compliance officer (CCO), chief audit executive (CAE), chief diversity officer (CDO), or chief human resources officer (CHRO). In hospitals and healthcare organizations, this also often includes a chief medical officer (CMO), a chief nursing officer (CNO), and a chief medical informatics officer (CMIO). In the United Kingdom the term 'director' is used instead of 'chief officer'. Associates include the audit executive, business development director, chief executive, compliance director, creative director, director of communications, diversity director, financial director, human resources director, information technology director, legal affairs director, managing director (MD), marketing director, operations director and technical director."