Part of the explanation for these differences is based on oxygen consumption. For every liter of oxygen you consume you will burn 5 calories. And because running involves the consumption of more oxygen it stands to reason that it also burns more calories. However, when the body weight is great and the physical abilities of the body are limited walking also increases oxygen consumption.
In general, controlling for weight, physical abilities and oxygen consumption the differences between calories burned running vs walking is that runners burn an average of 10 calories each minute while walkers burn an average of 5 calories per minutes.
But, let’s look at this equation. If an obese man with poor physical abilities walks quickly his calorie burn will be greater because of the increased oxygen consumption and weight. But as his physical ability increases and weight decreases the number of calories burned for the same perceived effort will be less.