In many cases a change in labels for Chinese states is used to distinguish between two different periods in the history of a state ruled by the same family, with the dividing point in many cases being the relocation of the capital, often due to conquest or military defeat. Hence the Western Han (capital at Chang'an) whose rule was interrupted by the "usurper" Wang Mang and and was restored to the rule of the Liu family in Eastern Han, which had its capital at Luoyang, to the east of Chang'an. Similar changes of name took place after the relocation of the Song and Ming capitals southward to after the conquest of Kaifeng and Beijing respectively. The term system is present in Chinese scholarship, but I am unsure whether it was used by contemporaries of those states.