I LEL@ this thread. C'mon Apoc this isn't complicated. To make it simple there was a time when descendants of the 2nd son were neither Senju or Uzamaki (or anything else). Like all people in human history, they changed over time due to differences in their social, religious, or ideological perspective. Or since this is about ninjas you could say different people had different ideas on what kind of jutsu were superior to others, and took different directions in their research of those jutsu. Some like to focus on sealing methods, others elemental jutsu like earth or water, and still others medical, yin/yang and other obscure methods. Naturally people of like mind tend to congregate together and share their methods with each other so that all can benefit. These people view their knowledge as superior to their brethren and an "us and them" mentality comes into place. They begin to associate less with these outsiders, and marry into their close allies. Over generations a web of marriages combines many families together, forever tying the descendants together in a loose confederation that we know of as a clan. Eventually the clans reach a point where they lack enough connection to their brethren that they simple drift apart. Whether this is a peaceful departure or a blood soaked one is another discussion altogether.
This topic reminds me of a trying to explain evolution to a moron. They inevitably respond back to you with the statement "Nuh uh, I ain't descendant from no monkey!" Like, not shit Sherlock. You came from a common ancestor that would later evolve alongside you into a monkey. Exact same shit with Uzumaki and Senju.