No, the wording in this picture both mean the exact same thing - how much work you are going to apply to the wall within a certain amount of time (A/t=P) (which is also called power. Horsepower (hp) can be expressed Horsepower = (P) 745 W and also torque can be expressed by watts P = T (torque) * 2 * pi * w. So by increasing horsepower the wall will travel further and by increasing the torque the wall will travel further.
And in the hitting-the-wall analogy, we're not assuming a dead crash with two static bodies colliding. We're assuming the engine is running full blast before, during, and after the crash. If the wall is indestructible (but is very heavy but can still move somehow by magic or whatever), HP is indeed how hard you hit the wall (max speed) and torque is how far you take the wall with you because the engine is still running. If you have minimal torque, you'll slam into the wall and make it recoil a bit but not much past that. If you have high torque (and same HP), you'll make the wall recoil the same more or less, but your engine will continue forcing the wall back.
It's like a shoulder tackle.
HP is your speed and torque is how hard you dig your feet into the ground to accelerate. With a high speed, you'll definitely knock your target back but once the target establishes itself, low torque (slippery ground, no cleats, whatever) means you won't continue pushing the target back any further. Low HP and high torque means you'll pretty gently hit your target but you will not stop. You will keep pushing your target back after the initial collision.
HP is your speed and torque is how hard you dig your feet into the ground to accelerate. With a high speed, you'll definitely knock your target back but once the target establishes itself, low torque (slippery ground, no cleats, whatever) means you won't continue pushing the target back any further. Low HP and high torque means you'll pretty gently hit your target but you will not stop. You will keep pushing your target back after the initial collision.