IOS – Why doesn’t the Apple Watch activity app count the activity recorded on the iPhone

Apple provide a support article to help improve Activity's accuracy, Calibrating your Apple Watch for improved Workout and Activity accuracy:

1. Bring your iPhone and your Apple Watch.
2. Find an open, flat area outside that offers good GPS reception and clear skies.
3. Make sure that Location Services is on. To check the setting on your iPhone, tap Settings > Privacy > Location Services.
4. Make sure that Motion Calibration & Distance is on. To check the setting on your iPhone, tap Settings > Privacy > Location Services > System Services.
5. Hold your iPhone in your hand, or attach it to your body with an armband (preferably) or waistband.
6. Open the Workout app on your Apple Watch, and choose Outdoor Walk or Outdoor Run.
7. Choose your goal, or select Open, and tap Start.
8. Walk or run at your normal pace for about 20 minutes.

You may find Adam C. Engst's Exercising with the Apple Watch: The Hardware insightful. Adam is a serious runner and he too noted the difference in distances measured:

Accelerometer -- Happily, the Apple Watch does have an accelerometer that enables it to detect your steps, from which it can determine both distance and pace, even if you’re not carrying your iPhone. It calibrates itself when you use it with the iPhone around, and I’m impressed at how accurate it can be. After a few runs, its numbers match quite closely with those collected by my Garmin and with the quarter-mile markings on San Francisco’s Bay Shore Trail, where I was running recently. Unfortunately, accuracy drops significantly if you run uphill (where your stride is shorter) or faster than normal (where it will be longer).

As long as you give it permission to access and change data in Health, it's all (steps, walking & running distance, heart rate, active calories, etc.) right there in Health. I know this first-hand, as a proud Apple Watch owner since April 24.