Apple's Health app for iPhone can track all kinds of fitness and medical related data, and from a variety of apps.
To allow Health to collect the data from App Store apps, however, you'll need to grant those apps permission to read and/or write to Health. That way, Health can keep your information absolutely private and in silos if that's what you want, but it can also act as a central repository and exchange for all your data. So, if you switch between fitness trackers, smartwatches, or apps, you don't have to start over from scratch each time. All your data goes with you.