Why do we start saying Mashiv HaRuach on Shemini Atzeres yet we do not say V'Sain Tal Umatar until Dec 4 / Dec 5 (In Chutz L'Aretz)? Why should they not be on the same day when they are similar Tefilos?
This question is, of course, the subject of a large part of the 1st Perek in Ta'anis. The reason we begin to mention Hashem's power of rain on Shemini Atzeres (Mashiv Haruach) is discussed in Ta'anis 2a-3a and is related to the Nisuch Hamayim in the Bais HaMikdash. The reasons we don't actually begin asking for rain then (V'Sain Tal Umatar)are:
The specific date we begin saying V'Sain Tal U'matar in Chutz La'Aretz is given on Ta'anis 10a. Rashi explains that this is later than in Eretz Yisroel because in Bavel they didn't need the rain as much and also that that is when the rainy season begins in Bavel.