1. The wall was all around West Berlin, separating it from East Berlin and the rest of East Germany.
2. There was a whole wide border defence strip, known as the death strip. The wall was just the inner most ("western") part of it. From West Berlin you could walk right up to it (though sometimes there was a thin strip of East Berlin strictly speaking), but on the outer ("eastern") side there was the considerable "defence in depth" and guards and fences etc. Basically, if you ever stood in front of the wall on the "eastern" side, you were either a border guard or about to be shot.
See pictures here:
https://allymalinenko.files.wordpress.com/2015/05/wall001.jp...
https://de.wikipedia.org/wiki/Datei:Bundesarchiv_Bild_B_145_...
http://www.tagesspiegel.de/berlin/berliner-mauer-der-geharkt...
EDIT to add:
3. Similarly, there was a 1400 km border between East and West Germany, which was also heavily guarded. It also had a border defence strip on the eastern side, up to 5 km (3 miles) wide, which incidentally turned it into a habitat for endangered species. While this "innerdeutsche Grenze" is less unusual and thus less famous than the Berlin Wall, more people died trying to cross it than at the Wall.
4. The crossings at that border were the stuff of spy movies: East Germany actually installed secret gamma-ray guns to detect people concealed inside vehicles. If someone arose suspicion and tried to flee with their car, there were 6 ton barriers, "Kraftfahrzeugschnellsperren", that could be catapulted across the road using hydraulic rams.