Measuring an instantaneous physical 'force' will not make it a moment any more than measuring pressure will give you a force, for example.
To "engineers" (which is a silly thing to say anyway) torque and moment are essentially the same thing, though may have slightly different connotations. A moment could be considered a force multiplied by a distance whereas a torque might be percieved as the action of screwing (no jokes thank you

) about a point.
Also, thank you for your crash-course in vector products, I will be sure to think of you in my engineering exams in future. Your explaination of why vector products are used is wrong and unhelpful and might make you appear slightly more credible thank you actually are. The vector aspect is inherent to the quantities used, but in this case is unnecessary as the direction of rotation (and hence torque) is obvious. Therefore the cross-product simplifies to a scalar multiplication, and your entire section was pointless.
EDIT: You mention above that you know "a bit about engines, engineering and such..." I'm interested to know what your engineering background is, and why you feel the need to try to overcomplicated things by introducing some of your 'engineering' (and i use that term loosely) knowledge, though the answer to those two questions may be unrelated.