The answer is yes and no depending on the time frame you are looking at.
You do not burn the EXACT same amount (even if you measure whole calories and not tenths or hundreths of a calorie) when you sprint a distance versus when you jog the same distance.
HOWEVER, the difference is minimal.
The RATE at which you burn calories is vastly different, but so is the time the burning occurs. A high burn rate over a short time and a low burn rate over a longer time yield about the same calories burned. ABOUT the same, not exactly the same.
Going from 12 minute per mile pace to 8 minute per mile pace will burn more calories per mile, but only a few more. A typical non elite jogger might go from 110 calories burned per mile at 12 minute pace to 115 calories burned per mile at 8 minute pace.
Wind resistance and a higher rate of metabolic processes raises the rate of burn, however once you get going faster than about 8 minute miles your running form gets more efficient and you need less calories (only a few less, but still less) to maintain pace.
If you factor in post running calorie burn, then running faster does burn more calories since your body will burn more calories as your heart rate descends from 180 after a hard sprint, than it would when your heart rate descends from 110 after an easy jog.
So, do you burn more calories running hard.
NO, IF: you measure a 10 mile run at 9 minute pace versus a 10 mile run at 6:30 pace, and don't count post race burn: then no, you did not burn more calories by sprinting the 10 miles. Your efficiency of form saved you more calories than extra wind resistance and increased metabolism burned. But the difference is less than 10 calories per mile.
YES, IF: you add in the post race burn, then yes, overall you did burn more calories by running 6:30 pace versus jogging 9 minute pace. But again the difference averages less than 10 calories per mile.
Moving a certain mass a certain distance takes a certain amount of energy. Efficiency of form, wind resistance, and metabolic factors can cause a slight increase or decrease in the amount of energy used.
So to the fat people of America: Go walk a mile a day. No need to run.