Sometimes quite a difficult thing to explain as they do the same thing but are measured in different ways. I wish i had college notes to refer to some of this but i'll do my best!
With torque, imagine you have for say a bar of metal. When you apply a rotating force what you get is an angle of twist(degrees) For an example of how much force you apply Say you want to get a nut off a thread that is solid on. Say over 1ft you apply 100 pounds of force that would equal 100lbft. The more distance you apply a load over ( say 2ft ) you would then have 360lbft of torque being applied.
With power, refering back to the original torque example, is how far in distance you go with that applied torque.
Pulling this off a random internet page ( and i hope its not a lie as it looks familiar to the equation i was thinking of.
Say you were applying 87.5 lb-ft of torque over a distance of 6.28ft ( 2 x 3.142 x 1 ) [ 3.142 is pi ]
torque * RPM * constant = hp
87.5 lb-ft * 60 rev/min * X = 1 hp
X = 1 / (60 * 87.5) = 1/5250
torque * RPM * 1/5250 = hp
hp = (torque * RPM) / 5250
This is why when motoring magazines they will put the power figure @an rpm!
Basically in referance to your original question, a diesel has a larger compressed explosion of the chamber in the cylinder due to it being turbocharged and diesel being a more explosive material under compression compared to petrol, so with the explosion in the chamber being larger, it will rotate the piston more forcefully, hence the larger torque figures!
Any questions

I'll refer back to some notes tomorrow but im pretty sure thats right!