Horde means nomad tribe, the word is originated from Turkish word orda , which refers to the royal court of the khan . It is also used in other Altaic languages , such as Oltin Orda (Mongolsâ Golden Horde) or Hos Orda (capital of Qara Khitan). Some Chinese scholars also think that the Youdu (belong to Huang Di /Yellow Emperor) is also originated from orda as the ancient books said Huang Di /Yellow Emperorâs clan had no fixed residence and Xianbei/Sirbi people called their hometown Youdu either.
Tributaries may refer to many factions around central China and paying tributes to the imperial Chinese court, including not only the nomad ones but also some moutain tribes , overseas kingdoms and even some Chinese warlords in the borderland .
No Chinese ruler fought all three groups at the same time in the history.
Tangut is a branch of Qiang , they rised as warlord when they assistanted Tang Dynasty in the battle against rebels.After Song Dynasty established, they didnât want to surrender so they established Xia Dynasty.
Khitan(a branch of Xianbei/Sirbi) also rised when Tang Dynasty still existed ,then established Liao Dynasty and occupied some regions of North China during the time that Tang Dynasty devided . Many years later , Song Dynasty united most regions of China proper and then faced Liao as their enemy who occupied North China regions.
So, as a Chinese dynasty , Song fought with both Tangut and Khitan at first.In my opinion ,to be exact, the later ones occupied but not invaded a part of North China as their ancestors had lived in those areas for hundred years or ruled those regions before Song Dynasty . However , the real invaders came soon. Jurchen tribes ruled by the Liao Dynasty/Khitan Empire rised up and contacted Song Dynasty to attack on their common enemy Liao Dynasty/Khitan Empire .Khitan was defeated by them but not wiped out. As a nomadic ethnic group , some Khitan people moved to Inner Asia , and established another dynasty called Qara Khitan or West Liao. So they no longer shared a border whith Song.Then conflict broke out between Song and Jin which was established by Jurchen. Jin defeated Song and occupied most of North China until Mongols rised up and destroyed them.
Interestingly , either rulers of Tangut, Khitan, Jurchen or Kublai Khan regarded themself as Chinese rulers . As results , Xia(Tangut) and Jin(Jurchen) are described as Chinese in the AOE2 scenario Genghis Khan , Khitay or Cathy became another name of China , and Yuan Dynasty(but not Mongol Empire) is described as an age of Chinese civ in AOE4.