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The units for torque, as you stated, are Newton-meters. Although this is algebraically the same units as Joules, Joules are generally not appropriate units for torque.
They are fundamentally different concepts. Horsepower is a unit of power which is the amount of work (W) which can be performed in a unit of time (t). Torque (tau) is a measure of force (F) applied across a moment arm (r). You can think of horsepower as literally the amount of power that a horse could perform. You can think of torque as the amount of twisting force on a crankshaft. In terms of real world results, torque is that neck-snapping feeling when you take off.