Your definition is correct in respect of Sephardim and Mizrahim. It is equally so of Ashkanazim which means German, most are not.
The term Sephardim and Ashkanazim is just a general term to distinguish those that follow the ruling of Maran or the Rema in terms of halacha.
I would agree there is none like the Rambam, but then he was special even then.
There have been many great Rabbi's
in all communities since then though, even if they do not match the Rambam.
And by the way all Jews are really Mizrahim , because we are all of middle eastern source. It is just persecution that drove us out to other countries, such as Bavel and Spain, Eastern Europe, North Africa and elsewhere.