Didn't know we were going to be talking about the two outside of how they relate to each other in our internal combustion engines.
I'll be more precise, then:
Torque and HP are not separate beasts. in the context of the internal combustion engines in our motorcycles that we are talking about
Torque is merely force (or work).
HP is merely a measuring of force (work) over time. in the context of the internal combustion engines in our motorcycles that we are talking about
By your own presented definitions, they are different. Torque does not include time as a factor, HP does. How can you maintain they are the same when you describe/define them differently? While it is true that you get both these factors at the same time in an IC engine (for non-zero values), it doesn't mean the two factors are interchangeable or mean the same thing.
Further, torque is not the same as work as for as physics terms go. Torque is the application of energy, work is when the energy is actually transferred. Beyond that, the availability of torque does not imply delivery of said force.
I don't see how this is helping other posters, though.
Back to the original point...
Higher compression increases the energy density at combustion time, allowing the engine to make more Hp AND torque. If you wish more of one than the other, then address fuel burn timing and duration in relation to crank position. If your burn pressures are concentrated while the crank rod journal is positioned near or around the 90 degree point, you increase torque, as that is where the lever arm has the most mechanical advantage for the twisting force. If you make the burn and duration timing more in line with the entire power stroke, you increase horsepower, as that maximizes the power duration. And yes, you can do both, but not to maximum advantage on both factors simultaneously.
Increased compression is an enabler for more power. Where, exactly, you maximize this power or force is to a greater extent dependent on engine timing factors, of ignition, cam, piston stroke, and breathing characteristics. But, it is more complex than that. Air has mass, and inertia. Velocity introduces other factors to charge density and burn timing.
Finally, light machines or machines that have low resistance to inertial change perform better with horsepower increases. Conversely, machines with high inertial resistance (e.g.) more weight) perform better with torque increases.
That's how I've come to understand it.
Feel free to argue.
Cheers,