Do you burn the same amount of calories running as you do walking the same distance?

You burn more calories per minute of exercise running than walking. However, if you run a set distance the workout is done a lot faster than if you walked the same distance. It's usually pretty much a draw between a short and high burn or a longer lower burn.

It would make more sense to ask if you would burn more calories by running or walking for a half an hour. You would clearly burn more calories by running for a half an hour than by walking for a half an hour. But walking would be much gentler on your joints, while running might be better cardiovascularly.