I don’t know what they do internally, but Loop Tools only works correctly on loops, so it probably only compares each vertex to two of its neighbours and do some ‘averaging’, while Smooth Vertex compares each vertex to all of its (selected) neighbours.
There still is a difference in calculations when used on loops between the two methods, I will see if I can find how the calculations of the Smooth Vertices are done, in the source code (of 2.91, but I don’t think that those have changed), but I can’t guarantee that I will find where the calculations are done.
The Loop Tools calculations should be easier to find…
