chanukiah

"On the first night of Chanukah, you put one candle on the right side of your Chanukiah."
"Apparently, Hannukiah is mostly an Israeli term. But I grew up Conservative in NY and we all used it as a term." (source)

Religious: Jews who are engaged in religious observance and have some Jewish education
Israel: Diaspora Jews who feel connected to Israel and have spent time there

The JPS Dictionary of Jewish Words, by Joyce Eisenberg and Ellen Scolnic, (Philadelphia, 2001).
The Joys of Hebrew, by Lewis Glinert (New York, 1992).
Dictionary of Jewish Usage: A Popular Guide to the Use of Jewish Terms, by Sol Steinmetz (Lanham, MD, 2005).

chanukia, chanukiyah, hanukiah, hanukia, hanukkiah, hanukkia, hanukkiya, hanukkiyah

Among contemporary Jews, a debate has circulated about this term. Some hold that it's incorrect to refer to the 9-branched Chanukah candelabrum as a menorah because that refers only to the 7-branched candelabrum which is a symbol of Judaism (see an example here). Others hold that both terms are acceptable to refer to the 9-branched candelabrum (see an example here). The Jewish English Lexicon favors the latter stance: menorah is the traditional term, and chanukiah is the more modern term, influenced by Modern Hebrew, which borrowed it from Ladino. Chanukiah is a subset of menorah, like square is a subset of rectangle.

Edit Something missing from this entry? Inaccurate? Feel free to suggest an edit.