I have updated a number of pages describing stamps, the Stamps Inspector, Stamps container, and the Stamps menu.
Currently (though this might change), the ordering of stamps in the Inspector and in the Stamps containers _are not synchronised. Changing the order in one does not affect the other. This can be confusing, especially if you have many stamps and wish to have better ordering, as it is significantly easier to do this in the Stamps container than it is in the Inspector. The latter only shows 6 stamp names at a time which is hard if you’ve >50 stamps to maintain.
Regardless, at present the Stamps menu always uses the list order as seen in the Stamps Inspector.