“There were a range of travel nuances. Allies (ie UK/USA/France) could quite readily get into East Berlin, but not beyond into the DDR.”
That was simply because the whole of the city of Berlin was classed as a military occupied city until the wall came down. When you went over to the east you really had to keep an eye on the boundaries and some were detained for getting it wrong. Another benefit was that the Vopo had no jurisdiction or any authority to stop the military so if they started the rule was for you to ask for a Russian officer. I only managed to get into the DDR once as I had to go to the Brixmis mission house in Potsdam and for that I got an ID card in Russian and got to go across the Glienicke bridge. The early 80s were interesting times.