If you don’t exercise at all and are starting a new running program to lose weight, chances are that you will lose weight just because you are moving more than you used to. One of the perks of using running as your method for getting into shape is that it raises your metabolism even after you’re done running, so you burn more calories throughout the day (especially if you run intervals).
Walking is fine, but you can cover more distance when you’re running, which means you will burn more calories in a shorter amount of time.
That being said, running does not always equal losing weight. Sometimes people think they’ve burned more calories than they actually have so they eat way more after and negate any calories that have been burned in their workout. You also have to remember that muscle weighs more than fat. As you burn fat and turn it into muscle, you may actually gain weight or stay the same (as far as the scale is concerned at least).
Just make sure that when you start a running program you don’t drastically cut your calories. You need to stay healthy and fuel your body so that you can actually run.