I would expect both to be reasonably accurate, so long as your stride length is constant and the watch is calibrated. If there is disagreement, I would tend to favour the treadmill's value. I don't have an FR235, but my VA3 expects to have its internal distance calculation calibrated to match the treadmill.
It does matter when you mix indoor and outdoor training, and when you try to aim precisely at a specific pace.
And in theory treadmill pace and distance is quite real, as it is the runner's pace relative to treadmill surface - just like for outdoor running. A well designed and constructed treadmill could give results identical (almost) to outdoor runs.
