This is the only thread you've posted that's inaccurate. The Senju and Uchiha were the first two clans. All other clans originated from them including the Uzumaki.
This Is My Own Opinion.
The Sage was NOT an Uzumaki because it was never said in the manga. All clans were born from the same Sage. So the Sage is also an Hozuki, a Yuki, a Nara etc. The Sage had two sons who were the ancestors of the TWO GREATEST clans that ever existed, The Uchiha and The Senju. Now most of you would ask the question of the other clans, how they were formed. Let me explain, you might not agree with this...
ALL THE CLANS WERE ALL FORMED FROM THE UCHIHA AND SENJU BLOODLINE AT SOME POINT. It's the ONLY explanation of how the other clans were formed. But the Hyuuga are more special because the manga said the Byakugan was formed from the sharingan therefore the hyuuga would be related to the Uchiha clan. The Uzumaki weren't genetically special at all...except for their large chakra and stamina. They were distant relations to the Senju just like other numerous clans. But what made them special was their vast knowledge of sealing jutsus. They endevoured to create and enhance sealing jutsus like Kuchiyose no jutsu, Death Reaper seal, Death reaper reversal mask seal, Jinchuriki sealing jutsu etc and others later learnt from their knowledge and advanced their jutsus to jutsus like Flying Thunder Jutsu, Edo Tensei etc
This IS just My Opinion By The Way.