Vernal Galaxy was a region of the Milky Way Galaxy, the third quadrant of which contained the Talos star group. (TOS: "The Menagerie, Part I")
The term "vernal" (a dated term meaning springlike or related to spring), is used in astronomical coordinate systems to refer to the point or region of sky defined by the vernal equinox. Its nature as a section of the Galaxy rather then a different galaxy was made clear by a statement from Captain Christopher Pike in "The Cage", where while on Talos he claimed he was "from a stellar group at the other end of this galaxy.".
The term "Vernal Galaxy" in the official Starfleet Command report was used in a sentence without a "the" preceding it, and was written completely in lowercase letters despite several important words being written in all caps.