They have different accounting cycles because a manufacturing company and a retail company distribute goods (and or services) in different ways. For example, a manufacturing company needs to take into account manufacturing costs. Retail companies would not have to do so because they don't manufacture products.
Remember to keep in mind that an accounting cycle includes all the actions that take place within a company. Thus if two different forms of companies record different financial transactions, it is only necessary that they would have different accounting cycles.