While the formulas are similar, Torque relates to the axis of rotation driving the rotation, while moment relates to being driven by external force(s) to cause the rotation. Moment is a general term and when used in context of rotational motion is pretty much the same.
Torque is $\vec{F} \times \vec{r}$. As @Apurba said, $\sum{\vec{F}}$ may not be zero. Moment = Magnitude of Force x Perpendicular distance to the pivot.

While the formulas are similar, Torque relates to the axis of rotation driving the rotation, while moment relates to being driven by external force(s) to cause the rotation. Moment is a general term and when used in context of rotational motion is pretty much the same.
Torque is $\vec{r} \times \vec{F}$. As @Apurba said, $\sum{\vec{F}}$ may not be zero. Moment = Magnitude of Force x Perpendicular distance to the pivot.