What is the reason for this difference?
If you examine the Thickness Mesh Analysis tool, you will see that it include a samples slider. This means that it uses samples to calculate the thickness. Sadly, it has a hard limit of 32 samples which doesn't produce very accurate results. However, I think the reason the values are not accurate is because it seems to cast rays in different directions and averages the thickness. If one or more of these rays end up somewhat parallel to the surface, they will cause the measurement to be inflated. Maybe, the minimum of the samples should be chosen, but please note this is just my guess. I didn't check the source code.
On the other hand, the measurements obtained with the Measure tool are typically correctly placed by the user to measure the minimum thickness which tends to be along the surface normal. And this explains why the tool does the sampling approach, because the minimum thickness is not always going to be along the normal, so the tool has to look around, in a sense.
As far as I can understand and verify with printed products, the effective thickness of the solid is the one measured with the ruler; do you agree with that?
I agree. Whatever you measure is definitely real and should match what you measure digitally with the Measure tool as long as both measurements are carried out along the same direction at the same spot.
I typically use the Analysis Tools to figure out possible problematic areas, and then manually verify that they are okay with the Measure tool. The Thickness Analysis Tool tends to falsely mark edges of printed pieces.