The search needs to be performed specifically by the light of a candle, and not by moonlight. Even though on the evening of the 14th the moon shines brightly, nevertheless a candle must be used because a candle works well for searching. The prophet also employed candles as a metaphor for searching (Tzefaniah, 1): "at that time I will search Jerusalem with candles."
It is not only better than moonlight, but is even preferable to sunlight. For example, if the search did not take place at night and needs to be performed during the day, one should not search the rooms by sunlight, rather he should light a candle and search by its light, for a candle can be used to probe cracks and crevices. Only on a porch, where at least one wall is completely open and there is much light, can one search by sunlight (see Tosfos in Eruvin 25.1).
The Rambam and Shulchan Aruch write:"If he searched by sunlight it is sufficient", which implies only post facto. On the other hand, the Talmud (Pesachim 8.1) explains this to be acceptable in the first instance, and the Tur writes similarly. There is one who understands their intent to be that the preferred practice is to search at night (Magen Avraham, comment 3). This explanation does not suffice, since we already have seen established that searching by sunlight is for those who did not search at night [and why then the repetition?]. Therefore it appears to me as follows: The Yirushalmi in the beginning of Pesachim considers that perhaps a candle is needed even in places where there is much natural light (see there), and though we follow our Talmud, nevertheless the Rambam was concerned for the point of view of the Yirushalmi, and so therefore uses a language that seems to imply post facto.
For purposes of searching by sunlight, a skylight would be considered similar to a porch if it much sunlight shines within. According to the Tur, the same would be would be true for an [open] window in a wall, though there are those who dispute this (comment 4 in the name of the Riv [?]). If the light is filtered through a glass pane it would be prohibited to use that light. [NOT SURE ABOUT THIS]
One should not search by the light of the torch, only by the light of a candle. The reason is that one is afraid to bring a torch close to cracks and crevices, and in addition it shines brightly backwards [toward the one holding it, obscuring the view]. Therefore it is not even sufficient as a device post facto, just as moonlight is not (comment 5). There are others who maintain that he would fulfill his obligation on a post facto basis (Eliah Rabah and M"CH??).
Now what exactly is meant by a 'torch'? This is when at least two wicks are braided or otherwise attached together. What is required is one singular candle which should be of wax, and not of any fatty or oily substance, for one will become distracted lest they drip onto his clothing or utensils. Should one use these he fulfills his obligation on a post facto basis. Therefore, if one does not have wax candles he may take candles made of fat or oil, though some do say he should not use oil since you will be concerned to enter into cracks and crevices, lest he spilled the oil (Magen Avraham). This though is only an additional stringency (so it also appears from the C"Y as well as the Magen HaAlef). It should be clear that one can fulfill this obligation on the post factco basis with the Naphtha we now use in glass lanterns, though one would certainly not fulfill his obligation with wooden sticks, as they are like a torch.