I took my iPhone and my wife's out walking this morning to make a comparison of the distances they recorded. The distance given by the Workout app on my Apple Watch and the hiking app (Outdooractive) on my iPhone were identical, presumably because they were both based on GPS. Unfortunately, I failed to get a reading from the hiking app on my wife's phone because it refused to record without me signing in, which I was unable to do.
I have now come to realize that the Health app on our two phones actually does nothing active. For example, you can't get it to record a walking distance upon request; it only records have far you have moved in total all day. It appears to just suck in data from wherever and summarizes the results on a whole-day basis and not just for a defined activity. Thus it does seem likely that distances measured by the Health app are only very approximate unless the app is fed data from a proper GPS-based tracking app, such as one of the many hiking ones that are available. I will have to get my wife to activate the hiking app she has but is not yet using.
Going back to my original issue, it seems that my wife's Health app only appeared to record the distance of our walks together because she only carried the phone while she was on the walk, whereas I keep my phone in my trouser pocket, so my Health app records the total of my day's movements. In fact, the distance of the walk in my case came from the Workout app and not from the Health app, so I was not comparing like with like. It does seem that any distance recorded by the Health app alone is only approximate as it is not based on GPS.
My thanks to everyone for their contributions to the problem I raised.
Brian Smale