Well, the explanation is both.
Persia is both an exonym and a division of Iran.
Like Holland vis a vis the Netherlands.
I find the sheer number of countries with English exonyms completely unlike their endonyms fascinating. Not the Polska-Poland but the really way out ones like:
Deutschland Germany
Sakartvelo Georgia
Hayastan Armenia
Shqiperia Albania
Suomi Finland
Sverige Sweden
Schweiz Switzerland
Zhongguo PRChina
Just think what fun far future generations will have trying to decipher the Free Republic “Comments” sections.....