As we turn the corner into the month of Hanukkah, a reminder for the gentiles:
Hanukkah is NOT “Jewish Christmas!”
No. No no no.
1) Christmas is one of the two most theologically important holidays in Christianity. Hanukkah doesn’t even crack the top ten, at least theologically speaking, in Judaism. (I would not, of course, denigrate those for whom Hanukkah is an important point of connection to Judaism, as that’s a different conversation.)
2) Christmas celebrates the miraculous birth of the Christian deity (at least into one of the deity’s three component parts) on Earth. Hanukkah celebrates a military victory by observant, unassimilated Jews over the Assyrian Greeks and assimilated Jews and the reinstatement of a Jewish monarchy. 
Birth vs Lots of Death (albeit of the Hasmoneans’ enemies).
3) For a very long time, Christmas has included the giving of gifts (though the form varied of course between times and cultures). Hanukkah didn’t, for much of its existence, beyond the provision of gelt (that is, money) to children. Many American and westernized Jews give gifts to their children these days, but that was largely borne out of making Hanukkah more appealing to make celebrating Christmas less appealing and even now it is far from universal.
4) Christians cannot work on Christmas (unsurprisingly, given its importance as a holiday), at least in the five largest denominations of the religion (other groups practices vary). Jews can work on Hanukkah (though they may leave early to light the Hanukkiah).
4a) Side note: Hanukkiah is the specific name for the candelabraum we use for Hanukkah (9 branches). Menorah translates to “lamp” and traditionally has seven branches but need not, necessarily. All Hanukkiyot are menorot, not all menorot are Hanukkiyot.
Now, none of this means that we don’t love and enjoy Hanukkah. We do! Fried latkes and sufganiyot, dairy products, child-appropriate gambling, songs….what could be better? But it is very, very much not “Jewish Christmas”.
