Как оказалось, це весьма волнующий и обсуждаемый вопрос. To make a long story short, в британском английском слово pail скорее архаизм, ассоциирующийся больше с nursery rhymes (Jack and Jill went up the hill/To fetch a pail of water), несмотря даже на такого кита, как Oxford English Dictionary (OED).

According to the OED entry, “The precise range of vessels denoted by pail, as distinct from the near-synonymous bucket, has varied over time, and there continues to be much regional variation. ”

Что касается американского английского:
If you could use can or cannister instead of pail, then you probably should not use bucket. If you could use basket or tub instead of bucket, you probably should not use pail.

Consider what happens when you go to an old-fashioned well to fetch water from it. There is a bucket permanently attached to the well, which you use to retrieve water from the bottom of the well. However, the thing you pour that water into to bring back with you would usually be a pail. That is, you use pails to fetch water from the bucket in the well. If you brought a bucket with you to get that water, it would be assumed to be larger than if you brought a pail.