Hyuuga are supposed to have branched off the Uchiha. The same way that Uzumaki and Senju are relatives (by sharing a common ancestor, or one branching from the other), Hyuuga and Uchiha are also related.
Uzumaki might have just come from some Senju who decided to start a new clan on some island, who either changed their surname to fit or had an Uzumaki parent. While Hyuuga might have been an Uchiha with a mutation. Those are just theories, but the prevailing one is that the Uzumaki and Hyuuga are Senju and Uchiha cousins. They aren't totally unfounded, these are all suggested in the manga. Kakashi called the byakugan related to sharingan and said one is a mutation of the other. Kushina said that the Senju and Uzumaki clans were relatives.