Just re-read what I wrote and I realized it makes no sense. Thanks for the correction. What I meant was in terms of fat loss it's about the same, unless you're sprinting or doing some other high intensity activity. When you walk, you're burning a higher proportion of fat because it's low impact and you're not taxing your muscles as much. When you jog, each step is like a plyometric push for your legs, so your muscles start to dip into your glycogen stores (quick fuel --> quicker recovery). You do burn more calories, but you burn a similar amount of fat as walking because the proportion of fat you burn is less.
Sorry for the confusion.