NGC 434 is a star cluster that is visible from Earth, in the space of the Tucana constellation. Within the Milky Way Galaxy, the star system of Horatius is associated with the stars of this grouping, although some of this group has been determined to be much further away, forming another galaxy. (TOS novel: Mission to Horatius)

Stars, systems and objects of the Tucana constellation
Gamma Tucanae • Horatius • Kappa Tucanae • NGC 434 • Rho Tucanae

The modern science of astronomy has determined that NGC 434, as viewed from Earth, is made up of a galaxy outside of our own. Since the Enterprise didn't leave our galaxy to access Horatius, it seems that some stars in our own galaxy are in a line-of sight between that galaxy and Earth when this grouping is referred to.