IMO, if one foot is on the ground at all times, that's walking. If BOTH feet are off the ground (even for a very short time), then it's running. The speed will vary depending on stride length and height. I also think that if you go a distance and any part of it is running, then you are "running". If you do a 5K in walk/run intervals -- that's running a 5K.
When I started running, 5 mph was fast. Then 5.5 was fast. Now I start on the TM at 6 mph and go up from there. You tend to get faster with training, but "fast" to you depends on your weight, running efficiency, and natural gait.
My running philosophy is that it's about having fun and moving and burning calories. You are going to burn pretty nearly the same calories over the same distance whether you run fast, run slow, or run/walk. It just takes you longer if your pace is slower, but the end result is just as good. So why stress over speed?
