Energy expenditure is calculated by how much distance you cover.
No, no it isn't... Energy expenditure is calculated by how much energy your body uses. Your body burns more to make itself move faster than it does to keep a comfortable pace for a distance.
Walk 1 mile, see how exhausted you get.
Now try to sprint a mile... Still convinced energy expenditure is more proportioned to the distance than speed?
When you walk:
-Your stride is MUCH shorter.
-Your legs don't use much of their motion range (the muscles can stay fairly relaxed, you don't need to lift your legs as high, you're not rotating those joints in the hip as much)
-Your heart rate is slower
-Your breathing is slower (heart rate and breathing are wired directly to the amount of energy you're expending)
When you run:
-Your stride increases possibly as much as 5 fold
-Your legs must stretch out more, using more range of motion
-Your heart rate increases as a response to the faster movement. This happens even if you only jog a short spurt. Your heart is wired to speed up as your body speeds up BEFORE you start getting exhausted and needing the blood-flow. It can happen in as short a time frame as walking up a flight of stairs. However the increase for a short period is much less than if you maintained that speed/effort.
-Your breathing increases, for the same reasons as your heart. That's right, just because you breath a bit heavier after walking up a few stairs doesn't mean you're out of shape. Your lungs are designed to work harder in response to that slight bit of effort increase.
What this means:
-Your heart uses energy, your lungs use energy. The increase in heart rate and breathing means your body is using more energy just to run its vital organs in response to your activity.
-You engage the muscles in your legs more. More muscles contract to move your legs a greater distance to widen your stride. This takes energy.
-You put more demand on your muscles. Since your stride can only get so wide, your legs must exhert more push within the same stride distance. As this push increases, you move faster. As you move faster, your legs must move back and forth faster to keep making contact with the ground in time. ALL of this takes extra energy to do.
So you see, running is significantly more demanding than walking. Regardless of how long or short the distance is. You would have to walk a few miles over the course of a couple hours to burn the energy you'd burn running a mile in 10 minutes (which is not an advanced goal).
When you start moving, you consume an innitial investment of energy to get the acceleration going from 0 to x. Furthermore you must invest additional energy to accelerate from x to y. When you slow down you do not recover significantly, you only ease the effort your muscles are expending, although this does allow some extent of recovery. In order to speed up again, you must expend extra energy to create that acceleration again. A car works exactly the same actually. All moving objects do.
When you run with a pace, you use that pace to your advantage, you're sort of able to coast your way through. Rather than having to use additional energy constantly to increase your speed, you can maintain a speed. This is because as you're running the ground is passing under you, the speed you pass over the ground is set at the speed you want to be traveling. Because of this, your foot will be moving backwards once it hits the ground regardless. Because you're running at pace, the speed your foot is moving is at the pace you want to be, so, less effort is required from that leg to make it travel at the speed you want to be at since your velocity is doing some of the work for you.
You can feel the power of this force for yourself. Sprint as FAST as you can. Now try to stop in place. You'll probably find that you can't, you get pushed forwards because of the speed you had going.
A good example of this is a bicycle. As you move faster, it becomes easier to push the pedals because the wheels are already moving, so the chain has to do less to move them. Whereas if you were to accelerate, or start from a stopped position, there would be a period of extra effort required to push the pedal to move the pedals to get the wheels spinning to that speed.
So the physics lesson: Acceleration ALWAYS takes more force than maintained speed.
Frequent acceleration and deceleration is a great way to waste energy.
This is why pacing makes such a huge contribution to how well a run goes for you.
As for the question at hand of track vs. tread. I think it's a matter of personal preference.
There's nothing to stop you from getting a really good workout on a treadmill. If you find the treadmill easier, make it harder, turn the speed up, use an incline, there's no reason to say that the treadmill is too easy to bother with.
The track will give you some additional more natural aspects (ie. direction changes, turns, etc), but the question is, how well do you really want to run? Do you WANT to be able to run through a natural course with diverse terrain? Or do you just want to get your 40-60 minutes of activity each day? A treadmill will definitely train your ability to run, but a track will adjust you to the aspect of the track.
Furthermore, the treadmill makes it easier to push yourself harder. On a track, you're free to slow down, free to take it easier on yourself, free to do what you wish. On a treadmill, you can keep yourself going easier. It's easier to push that little extra bit of distance when you have a machine that'll force you to run at speed. You can always tell yourself "I'm just going to leave the machine running like this and bide my time until I've covered the time required to meet that distance mark regardless of what I want to do". This can be very helpful for someone who isn't accustomed to the mental aspect of running. It's like having a coach who will yell at you every time you slow down. Except instead of yelling at you, the treadmill trips you, or throws you off. Use common sense of course, but in this respect, the treadmill can be an advantage to training yourself mentally for running.
So overall, both methods have the capability of giving a workout which will push you to your limits. The track DOES have some additional features which will deliver more training than the treadmill. It's impossible that these features wouldn't require a bit more energy to work with, although how much energy is up for debate.
The fact is though, running is still running. Whether it's on a treadmill or a track you will still get a good workout, and a treadmill will offer more than you need to help you achieve good fitness. Unless you're going to be running on a track, it's not crucial that you train yourself on a track. The training you do on the treadmill will still improve your performance on the track, even if the track still seems much harder to you.
Use whichever makes you happiest. If you just want good health, both will do the trick. If you just want to get more exercise in less time, run faster. For someone who's JUST trying to keep their body in shape, there's no need to go out of your way to adapt to a track.
However, if you've just been walking on the treadmill for more time going the same distance you'd be running, any improvement in fitness will be minimal at best. The distance between you and the starting line wont tell you how much energy you use. It's the sweating, breathing, and heart rate which tell you how hard you're working. Power walking is a bit better, but even so, a 1 mile power walk does not equal a 1 mile run whether it's on a track, or treadmill.
As far as the displays on the treadmill go... No, they are not accurate.
No display on any exercise machine is accurate. In fact, most of the monitors you can buy separately wont be accurate either.
The pulse monitor:
-Simply put, it's wrong. Those little hand-grip pulse bars they put on treadmills are junk. They just don't detect your pulse accurately enough to count it properly.
-The sweat on your hands will actually interfere with the machine's ability to detect your pulse.
-The finger clips aren't much better
-ALL heart rate monitors have a margin of error. Even the high-quality chest-strap monitors can pick up and display a false pulse reading, however the chest straps have a much lower margin of error, and will give you the most accurate reading possible without access to medical equipment.
-In my experience, the handle-bar readers are less reliable than your own judgment.
Calorie Counter:
-Wrong.
-There are far too many variables that determine the amount of calories burned that a treadmill can never account for. I 100% guarantee that your reading is wrong. It could be higher, it could be lower.