Assuming you are not holding hand rails part of time preventing some steps from being recognized, which is less likely on a run, you probably just need to adjust your stride length. A default is set, based on your physical data (height, age, etc) but you can adjust; plus might have different stride length on treadmill than regular running.
On phone app:
days of exercise tile > gear icon near top right > stride length > running stride length
As first estimate, I would just multiply the value there by 1.11 i.e. (5 / 4.5). Then you could fine-tune it as needed.
P.S. stride length is used to convert step count to distance when not using GPS.
Before posting, re-read to see if it would make sense to someone else not looking at your Fitbit or phone.
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