So is the “Health” App a Apple App? I run just about every day!I’ve noticed over the past year or

It is an Apple app. But, the health app also aggregates information from multiple devices and apps. I've had instances of some runs being, well, not quite double counted because of an app and Apple's built in tracking. In theory selecting your app priority in the health app helps. I'll still find some errant data from time to time but it is easily edited. You also have to consider which measures you're using. For example, the walking and running distance aggregates throughout the entire day. So those numbers may be off because you walked a mile during the day too.

Go to Settings > Health > Data Access & Devices to fine tune the information any apps share with health. This guide should help: https://support.apple.com/en-us/HT203037

I used endomondo which is now map my run. It's really pretty close for distance and I have that app tied into health so it writes the run distance, etc. into Health. There is some natural variance depending on the side of the street, etc. which can add up over a distance, certainly not an extra mile on 3 but it could be a small, but surprising amount. I have a measured 5k and I'm about a quarter mile from house to start. So roughly 3.6ish miles. I'll get reported back anywhere from 3.5-3.7 most days. Sometimes that's me wandering back and forth across the road or forgetting to start tracking, but it's good enough for me.

Sorry. Should have been clearer. Endomondo has been turned into MapMyRun https://apps.apple.com/us/app/map-my-run-by-under-armour/id291890420