Chief Executive/Managing Director/CEO?

Hi,

Could someone please advise me the difference of the meaning/nuance among "chief executive", "managing director", and "chief executive officer"?

I founded a law office (in Japan) and am wondering what title would be appropriate for being a top of a law office (for an English page of its business website). Though there are several lawyers working for it, they are not partners, so I guess "managing partner" is not appropriate in this case.

Thanks in advance.