"From the bridge we are runnig to the island, not into the house."
Translation:A hídtól a szigetre futunk, nem a házba.
"from the bridge" could be either hídtól or hídról. It is not clear, if we were on the bridge or close to it. The same for "to the island": szigetre or szigethez
Yes, Hungarian is very specific in this regard. English can only assume that we are starting on the bridge, otherwise we would already be on the island. And that we arrive on top of the island, otherwise we are either in the water or still on the bridge. These are assumptions that are usually correct.