They've lived in southern Texas for years, but have never been south of 'the border'. [=the U.S. border with Mexico]
The neighborhood 'is bordered' by Main Street on the north and the river on the south.
She's from northern Montana, near 'the border'. [=the U.S. border with Canada]
(..) Young Mr. Frodo here,he's cracking. And proud of it. -Cheers,Gaffer. -Cheers. It's none of our concern what goes on beyond our borders. Keep your nose out of trouble,and no trouble'll come to you. -Good night,lads. -Good night. Good night,sweet maiden of the golden ale. (..)2001 The Lord of the Rings: The Fellowship of the Ring