Ner Shel Nachri Diloh Shovas one cannot use for Havdalah. What is the difference between this and a Ner of a Choleh that is permissible? I see the Achronim deal with this, but I have not found a satisfactory answer.
chaim ozer shulman
Rav Yosef Engel (Asvan d'Oraisa 10) suggests that it is evident from here that the Torah not only prohibits the action of lighting a candle on Shabbos, but it even prohibits the candle from being lit (unless the Torah specifically permits it, in a positive manner, as is the case with the Choleh. Not so with the non-Jew, where the Torah simply does not prohibit it, but does not permit it). This is why the non-Jew's candle is classified as Meleches Aveirah. However, there are a number of problems with this interpretation, though.
The simple unsderstanding is that the candle must have not been used for a purpose which is prohibited for Jews to use on Shabbos, since they are the ones making Havdalah. It makes no difference who lit it, as long as it was permitted for Jews to do so.
BE well,
-Mordecai