I agree that the two clyindrical wood boxes are firkins .
I'll suffer the slings & arrows for my following suggestions :
Perhaps the 'splattering' of spots on the exterior of your butter molds is from cooking debris & could be gently cleaned (cleaning with the grain of the wood only) with a mild solution ( I use Orvis Wa ) & not much water (damp cleaning , not immersion) .
A soft toothbrush & some patience might give you positive results (try cleaning just one little spot first , before commiting to a method that may not work on the problem) .... others might use a super-fine grade of steel wool to hasten the process .
I've seen folks get pretty darn good results with food debris-cleaning using (cringe) Oxy-Clean in a mild solution ...
As waywardangler mentioned , if you've got 'spalting' , it's pretty much a condition that is permanent .
I have seen spalted wood antiques treated with wood bleaches (which all seem to only lighten both the spalting & the undamaged wood) & stained darkly , in an attempt to hide their condition .
I'd suggest that you give your wooden items , after they've been cleaned & fully dried , a good wipe-down with food-grade mineral oil (pharmacies carry it) & another good wiping to remove any excess oil .
The wooden items seem dried-out & I bet they'd like a drink !
You could also use a common-brand wood furniture paste wax like 'Johnsons' , if you have a mind to .