On Shabbat one may not use a wick or oil that does not give an even, bright light, in order to prevent the light from flickering and going out. On Chanukah, however, we may use any wick or oil. The mitzvah of the Chanukah lamp is that of kindling the lights, and if the light goes out it may be re-lit (though not on Shabbat).
According to the S’fat Emet this represents two different kinds of Jew. There is the “flickering” Jew whose Shabbat-Jewishness wavers. They deserve praise for trying, but they miss out on the day-long holiness of the day. On Chanukah the “flickering” Jew is not such a problem, and if he/she wavers in observance they can re-light their Judaism and try again.