Torque and Horse Power are closely related. How they relate depends on the application.
As mentioned earlier, older saws had different configurations, and often had less over square motors. The 3120 has about 2mm more piston width than a McCulloch 797, for example. This gives more time for the cylinder to fill up, and more time on the power strokes, but often physically relegates the engine to lower operational speeds(at least in most saws it does).
But the other reasons previously stated certainly apply.
And now for some basic physics...
Torque is the turning force an engine has over a given distance(not time), often measured in foot pounds or Newton Metres.
Horse Power is energy, or the ability to move a mass over a certain period of time(1HP = 33,000 ft·lbf/min or about 745 watts/.745KWH, or 550 ft-lb/s)
Or, the amount of force that can be exerted over a certain period of time. IE - the amount of work something can do.
'Force' and 'energy' are not interchangeable, a mistake many folks make. Torque is a force. HP is energy. However, both can be made to do work(energy). Read on.
Horse Power is actually very close to the amount of work a healthy draft horse can manage for limited time spans.
In other words, when it is stated that an engine produces "X amount of Ft Lbs at Y amount of RPMS", that is the actual amount of force that motor has at that given engine speed.
When it is stated that an engine has "Y amount of Horse Power at Z RPMS" It is saying that at the engine speed of "Z" the motor is capable of producing Y times 550ft-lbs/second of force. This is a measurement of potential energy rather than the actual force the engine is putting out, really. Well, at least technically speaking. Read on.
Horse Power only measures what an engine can do during a certain period of time. HOW it does it is hugely dependent on what it has to do, and what it has to do it with. In order for HP to be relevant, you need to find a way to 'put it to the pavement' as they say in the car biz. Or, in the saw biz, put it in wood. In order for a saw to cut wood it has to pull a chain through the wood while it rides on a bar and around a drive sprocket(the gear on a saw), and engage a clutch(the drive mechanism), running off of the prop shaft/crank shaft(this put's two 'simple machines' together, the wheel and the fulcrum/lever). All of this puts a load on the saw engine.
Now, to get that engine to do that work:
Gearing - gas/petrol motors need it. It turns HP in to torque(sort of like bending space and time... sort of). Saws are all about turning HP into torque(well, most petrol engines are).
You may have heard that DC electric motors can produce a large amount of torque. They do this because the power comes from a constant source. In this case, a direct current of electricity. Gas engines, by comparison, are driven by the impulse of an explosion. For a 2 stroke motor, the amount of time it spends producing power VS a DC engine is nearly non existent. It has a short, single power stroke for every revolution of the crank shaft VS the constant power pouring into a DC motor effectively nearly 100% of the time(and please for the sake of argument, lets not get into DC motor design, or brush configurations, etc). Fortunately, 2 stroke engines make math easy. For every revolution, there is a power stroke. If you have a 7 pin sprocket, it pulls 7 drive links per revolution. An 8 pin sprocket pulls 8. Obviously, an 8 pin sprocket requires the engine to do more work every time it has a powerstroke since it pulls one more link per revolution. The more powerstrokes a saw motor has for whatever work it has to do, the more torque it can produce. The more torque that engine brings to the table(or is rated at), the less gearing it will need vs a similarly(method-wise) rated engine with less torque. Thus a 7 pin sprocket allows a saw engine to produce more torque at a given rpm vs an 8 pin since the engine is producing more power strokes per revolution of the sprocket = more turning force= bending space and time(but not really). At 10,000 RPMs it starts to add up. With more torque, a saw may be able to cut more aggressively, or bog less often, and even though it is pulling less chain at a given RPM, it may be able to spend more time cutting VS bogging, or it may be able to hold a higher RPM in the wood before bogging, use deeper rakers, bigger chain, longer bars, etc etc. But this all depends on the motor. A 50cc saw will like to see a 7 pin most of the time. A 120cc saw might pull a 9 pin fine with a 36" bar buried due to it's torque; it may not require much more multiplication. Length of chain, bar, cutter type and raker depth etc etc play a part. It also may hypothetically explain why a 50cc saw that is ported may still have difficulty pulling a 32" bar through large timber even if it rates at the same horse power as a bigger saw like an 80cc saw. That 80cc saw may simply have more torque, and with the same HP it is able to apply more force over a given time period. It's all so complicated. But hopefully, now you understand a bit more about HP vs torque, and how a saw uses both.
Ugh, it's passed 3AM again. I'm gonna pass out.
