姓(ancestral name) originated before 氏(clan name), when the society was still a matriarchal society and thus most of the original ancestral names were feminine. ancestral names of children used to be the same as their mothers instead of their fathers as it was a common thing in a matriarchal society for children to not know who their father was. However, as the society slowly turned into a patriarchal one, ancestral names were more or less fixed for every children. As the patriarchal society was established and as children from the same family were separated due to various reasons(war/migration/politics etc.), they formed their own clans. In order to differentiate their clans from other clans with the same ancestral name, they came up with clan name of their own. The clan name is usually the name of the region their clans were formed in or the position in court of any notable ancestors, which means that the clan name is much more dynamic than the ancestral name. By the Han dynasty, the dynasty that came after Qin, the line between ancestral names and clan names were blurred and were slowly merged.
For example, Ying Zheng(嬴政) has a ancestral name of Ying(嬴), which originated long ago and the clan name of Zhao(赵), which was a branch of the ancient Ying family which migrated to the Zhao area somewhere in history. Men from the the time of Kingdom manga(era of the warring states) were referred to by their clan name instead of their ancestral name so Zheng will be referred to as Zhao Zheng(赵政) then. People today refer to him as Ying Zheng(嬴政) because clan names were removed from Chinese names entirely today. For Ying Zheng’s case, he is indeed a distant relative of the royal family of the state Zhao as their ancestors from many generations ago were actually brothers, and thus they share the same ancestral and clan name. Most commoners in the era of Kingdom manga(era of the warring states) do not have any ancestral and clan names, which is why most characters in Xin’s unit, including himself, were only referred to by their given name.
Information from: http://zh.wikipedia.org/zh/%E5%A7%93%E6%B0%8F