Calorie burn is a function of distance covered, not your speed.
While you may have gone a little faster on the walk/run to cover it in only 30 minutes, and during that time you burned "more calories" per minute, you spent less total minutes exercising. So it balances.
When you get faster with the running you'll start to notice a bit of difference. But right now at an average page of 15 minutes per mile, that's still a "walking" speed and won't register as a run. The system thinks you walked. Whether you walked 'quite fast' or walked 'quite slow' doesn't matter because of the balancing out of time spent.
Running does burn more! But you need to spend more time running and get a bit faster in your running before the system will classify that amount of distance over that time as a "run".
Deb, in New Zealand