"Район" is a group of settlements, which counts as a small administrative and territorial unit in Russia. "Регион" can be defined as a "район" that covers a large area and has its geographical boundaries. In "регион" there is also a certain economical, social and cultural system of interconnection. "Округ" can be similar to "район" if we speak about a small administrative unit (for example, there are 10 of them in Moscow) and to "регион" if we speak about the whole country. "Край" is a huge administrative and territorial unit (there are only 9 of them in Russia as far as I know). Nowadays "край" as an administrative unit doesn't differ from "область" and it got its name from those outlying districts of the country. So it’s something like that ^_^