Not sure how/why as it seems both Health app AND Health Mate would be gathering the data from my Apple Watch, but the two apps are always a few hundred steps different (Apple being less; Health Mate a couple of hundred higher.
Earlier today I uninstalled Health Mate and reinstalled; no change in steps not the same for today.
Steps are an approximation based on the swinging of your arm.
You may be better off measuring actual distance uing an app like Strava or Nike Run Club.
10,000 steps for general health is a wide open target and includes general movement during the day.
No two apps will estimate it the same way. If correctly installed, any sport app will feed the Health app in preference to the standard workout, but I am not familiar with that app.
Check the data sources in the steps section in Health. The Health app should take data from either source but preferring the first in the list.
Fo any queries contact the developer of the third party app.
How to contact an app developer - Apple Support
Health App Step Tracking NOT matching Steps recorded in Health Mate
