Also were these terms used by the people living in those eras? Would a Roman during the republic referred to themselves as the ancients and would a Holy Roman emperor have referred to himself as a Medieval monarch?
Chinese history is classified into periods like Medieval, the Dynasties are just another way of categorizing conveniently that can't really be replicated over Europe because it didn't stay unified for long or across several periods. Within individual nation's histories we still do classify things by dynasties when available(e.g Plantagenet, Tudor, or Stuart England).