Step Counter on Phone

I think they use their orientation sensors to sense rhythmic motion that matches some profile of walking/running and count steps accordingly.

Wife has that going on her phone. We are in Europe and have been getting about 20,000 steps per day with a high of 32,000 one day. Her app converts that to miles but my quick calcs say the app is about 20% too high.

That could just be a difference in the algorithm used to determine what constitutes a step between different software analyzing movement. You shouldn't be concerned with the exact amount of steps you are taking because that is more or less meaningless. Running steps are worth more than walking steps for instance from a fitness perspective. I find it better to pick one tracker, which will consistently measure your activity level in "steps" and view "step count" as level of activity for a given day instead of looking at it as the exact amount of steps you took. Combined with other sensor data from a wearable, like time in elevated heartrate, sleep, etc. you can get a better picture from a fitness perspective of how well you did. If you are trying to compare steps from one device to another then you lose the consistency due to how differently those algorithms might measure activity or "steps".