Alcor is indeed part of the Ursa Major constellation, designated as 80 Ursae Majoris, while Mizar is Zeta Ursa Majoris. The confusion arises from the fact that Alcor is not one of the seven brightest stars commonly associated with Ursa Major, known as the Big Dipper or Plough. Ursa Major contains many more stars than just these seven, with historical catalogs listing around 86 visible stars. The naming conventions and cultural interpretations of the constellation vary, leading to different colloquial names in various languages, such as "Big Cart" in Polish and Portuguese.