During the time of the division of Germany, both before and during the Berlin Wall era, there were 3 canal routes, 3 rail routes, and 3 road routes linking what became West Germany with West Berlin. The theory being, during the 4-power occupation of Germany after WW2, that since Germany as a whole, and Berlin specifically, were both divided 4-ways, and since Berlin was wholly within the Soviet zone of Germany, then there should be routes to ink each of the 3 western occupation zones of Germany to their respective zone in Berlin. (And there were 3 air corridors too.) If you look at maps of the routes, the practice wasn't as neat as that of course, for all sorts of reasons (including that the French occupation zone had no border with the Soviet zone). I'll leave out the other complications such as the parts of pre-war Germany that were detached from Germany at the end of the war and didn't count as part of these zones, and the fact that other allied countries were allowed to have their troops "in charge of" bits here and there.One metro line of the west Berlin network had a section, without stopping, in the east Berlin territory.
And of course, trains from west Germany to Berlin did not stop anywhere in east Germany.
I’m not aware of any public transport line of east Germany that wandered into the west.
As I understand it, yes, the trains from West Germany through the DDR to West Berlin didn't have station stops in East Germany, but I believe they did stop for East German guards to check them at the border at each end. On the road routes, you weren't supposed to turn off the route, but obviously it couldn't all be fenced off and guarded the whole way, and the routes couldn't be fully segregated from the rest of the East German road network. Some comrades of mine from West Germany were involved, during the Berlin Wall era, in smuggling printing equipment to comrades in East Germany, by way of driving along one of the transit routes between West Germnany and Berlin, and stopping briefly to unload crates in a pre-arranged layby... Apparently it wasn't as difficult to do such things as might have been expected- it just took organisation and nerve.