So ok, we have a few different variations of teleporters though. There is the 935 model teleporter, as seen on Kino and Der Riese. Then there's the "five" version. Then there's the Gersch device. Finally we've got the Origins version.
I always imagined that the progression of their development went as follows: (pretend origins is relevant for a sec)
So group 935 discovers the Origins portals, and studies them to come up with the basis for teleportation. They create a concept for a similar "gateway" style teleporter which ultimately gets scrapped. That scrapped model is seen in the Nscht Der Untoten loading screen. Then they take a new approach and make the Der Riese model. Anyway after the fall of the Nazis in WWII, the allies seize 935 documents. They decide to try to create their own teleporters, but instead base their prototypes off of the initial "gateway" style teleporters. That's why the teleporters in "five" behave more like the ones from Origins. The soviets made their own attempt at re-creating it, in the form of the Gersch Device. The Moon teleporter has a classic 935 model (obviously).
Oh yeah, then there's the Denizens. That's probably because they are creatures mutated by 115, and the earth is enriched with it from the missiles.