A border is a line that separates two countries or other political regions such as states or counties.

1. Stanley wanted to spend the night across the Florida border.
2. …his parents’ crumbling ancestral home somewhere on the Welsh border.
3. So, legally or illegally, they crossed the border.

A boundary is a line that separates any two areas, for example towns, farms, or countries.

4. Matthews showed us a fine old hedge which once marked the parish boundary.
5. In international law, three miles is generally taken to be the boundary of a country’s airspace.

You refer to a border as a frontier when it is guarded and separates countries which have different political systems or are in dispute about something.

6. Military activity on the frontier diverted troops from their internal security role.
7. I have to get off the train at the frontier and cross on foot between the guard posts.

A frontier can also be a limit beyond which nobody has explored or established political rights.

8. Space will not be the last frontier, it will simply be the next frontier.