A milk pail would be taller than it was wide I think? Aren't these wider than they are tall?
Whatever they're modelled on, it looks to me as though the cut bands are probably meant to replicate some kind of vessel of banded wood. (wine cask, whisky cask, coopered pail etc) but are also a decorative feature to use their cutting techniques.
I think it's possible they're butter dishes and should have lids and underplates.
I can't imagine the size of the one in the Neuwelt book but at 11cm high it doesn't seem huge. They describe that larger one as a bread bowl. The other has no description. Mine is the same shape but much smaller and I thought perhaps a salt.
I suppose it depends how their bread was traditionally served at the time. Different geographical regions, different customs and also a different time period.