First some definitions:
Walk: to advance or travel on foot at a moderate speed or pace; proceed by steps; move by advancing the feet alternately so that there is always one foot on the ground in bipedal locomotion and two or more feet on the ground in quadrupedal locomotion.
Hike: to walk or march a great distance, especially through rural areas, for pleasure, exercise, military training, or the like.
Run: to go quickly by moving the legs more rapidly than at a walk and in such a manner that for an instant in each step all or both feet are off the ground.

I’ve never been big on hiking per se as a work-out, and while I used to run 4-6 miles three or four times per week, those years are long past. I regularly walk the canyons here and it’s okay for getting my heart-rate up. Lately I’ve been doing that 4-6 miles at a walking pace up/down hills. That said, I’ve read some relatively recent research that indicates your heart does best with something like wind-sprints —
Wind-sprint: a sprint, usually run several times in succession as part of a conditioning program, to develop an athlete's wind, speed, and endurance.

Running, sprinting & walking aside, I prefer lifting weights (ie., resistance training) to endurance running/walking. If you’ve ever done squats in a gym (most folks don’t have a squat rack and an Olympic bar in their home gym) you’ll notice your heart-rate climb significantly, similar to how it responds with wind-sprints. Then you stop and your heart recovers, then you do another set and another....

I mention squats because it’s considered a whole body exercise, meaning you have a lot of your muscle groups involved and that in turn burns more calories.

Do what you can, don’t hurt yourself. Knee injuries are what convinced me to stop running. When I started lifting, my leg muscles (all those little guys around your knees) strengthened and I was able to run better when I needed to, I just didn’t make a habit of it.

YMMV