No definitive answer but an observation. To me a bucket means an old fashion container, made (by a cooper) of wood secured by bands of wood or metal. A pail is a modern bucket, made of metal, plastic, etc.
On the other hand, in my youth there was a garbage pail insert in an outside disposal container which was sunk in the ground, usually somewhere near your back entrance, and you put daily kitchen garbage in the pail outside and a garbage man came in a truck once a week and emptied the pail. In northern climes you had to be sure a path to the garbage pail and around the garbage container was shoveled for the garbage man or it didn't get collected.
Nowadays there are plastic bags and garbage/trash cans that you put out for curbside pickup. Far more sanitary but you must put the trash curbside. No longer do trash men enter the yard and take the can to trucks to empty then return them to where they picked them up!
WWII changed a lot of daily life.
