Your information about the menorah and hannukiah is mistaken. A hannukia has 9 branches and its ninth branch is the shamash. A menorah only has 7 branches.
Actually, in classical Hebrew a "menorah" refers to a candelabrum of any sort, not just the 7-branched one used in the Temple. A "hannukiah" or "chanukiah" is a Modern Hebrew term for a menorah with nine branches. It is a neologism; the term did not exist until Ben-Yehuda came along in the late 19th Century.
In the United States (where our site is based), the Chanukah candelabrum is almost universally referred to among observant Jews as a menorah, not a chanukiah, following the traditional usage.
Finally, every major English dictionary we've consulted includes among the definitions of "menorah" both the nine-branched candelabrum used on Chanukah and the seven-branched one used in the Temple.