OK we've got a lot of different answers but here's my attempt at clearing things up:
You are always burning fuel (mostly fat/carbs) no matter what you are doing - even sleeping. So yes, you are definitely burning some fat when you are running.
Here's some basic principles:
1. The longer you run, the more fat you will burn.
2. The harder the exercise, the more total fuel you will burn
3. However, with very intense exercise, the proportion of fats burnt is not as high as compared to carbs
So a long distance "fast jog" would probably be the best for you to burn more FAT.
Now to explain the "building muscle" part:
1. Muscle remodels itself according to the amount of stress (exercise) we expose it to
2. Muscle growth only occurs if the stress is larger than what it's usually exposed to.
3. Therefore with heavy exercise, there's even more strain, so there's even more muscle growth
So if you are new to this exercise, it's probably a large enough "stress" that will cause muscle growth. If you've been doing this for 6+ weeks already, then you should have "adapted" to this stress and you will no longer be building muscle.
For someone that's a weight lifter, it's going to cause muscle loss because the stress is a lot tinier for them in comparison to what they're used to.
Even though it is normal for weight to fluctuate, you should always monitor it at the same time every day (preferably mornings). Changes in your weight can occur across the day just because of eating/drinking. E.g. 1 litre of water will make you put on 2.2 pounds.