The Hanukkah menorah and the yahrzeit lamp are both flames lit in the home rather than a place of worship, and comparing the rules that govern them shows how differently a single act, lighting a flame, can be weighted depending on what it marks. Hanukkah lighting follows a strict published sequence: one candle the first night, an added candle each subsequent night for eight nights, using a ninth helper candle, the shamash, to light the rest since the Hanukkah lights themselves are not to be used for any practical purpose such as reading, and the lamp is traditionally placed in a window or doorway visible from the street specifically so that the miracle it commemorates is publicised to passers-by rather than kept private.
A yahrzeit lamp observes essentially the opposite logic: it is lit for exactly twenty-four hours on the anniversary of a parent's death, privately, with no public display intended, no fixed liturgy attached to the lighting itself, and no obligation beyond the household of the mourner, its sole purpose being remembrance rather than celebration or publicity. Both practices sit within the same broader Jewish framework in which fire stands for something beyond illumination, the miracle of the oil lasting eight days in one case, the enduring flame of a soul in the other, a rabbinic image, that a person's soul is the lamp of the Lord, drawn directly from Proverbs and applied specifically to yahrzeit observance, but the two practices could hardly differ more in tone, one lit outward toward a community and one kept quietly for a single household.