Learn English – What’s the difference between federal republic and commonwealth

Cutlery has two definitions: 1. cutting/edged implements used for serving or eating food; 2. eating utensils in general. Without further context, an American is likely to assume the first definition (knives), while a Brit is more likely to go for the generic meaning. Silverware also means eating utensils, especially silver-colored ones, though nowadays, most silverware is not actually made of silver. An American synonym that does not imply anything about the silver content (or lack thereof) is flatware.

Crockery is completely different: in British English usage, it means the things on the dinner table that are usually made of china or porcelain -- plates, bowls, saucers, cups, serving bowls, etc. In American English, crockery is used for certain earthenware cooking pots, but given enough context, an American would probably understand crockery used according to the British definition.

I feel like the word pail almost always describes a metallic object, shaped in a near-cylindrical fashion. Sometimes a pail can be wooden, but rarely. Buckets can be made of any old material, especially plastic, and can be shaped more strangely than pails.

In addition, bucket has some interesting and amusing uses in slang:

1. In its plural form, it can be an expression of unalloyed happiness. It comes from the slang term from having just scored a field goal in basketball. For example, if you had just won something unexpected in the mail, you might say "Buckets!" to celebrate it, just as you might having scored playing basketball.
   

2. It can describe a particularly decrepit vehicle, a hoop-ti; most often applied to vans.

3. It's an urban slang term for urban-style hats, typically wide-brim and loose fitting.

4. It's an urban slang term for expensive rims on a car. As so memorably used by the rapper Yung Joc, "...ride around slow so you can see the buckets on my feet [tires]..."
   

Pail, sad to say, is utterly lacking in this regard.

EDIT: Taking a look through Google's N-Gram viewer, it's not hard to see why:

This comparison of bucket and pail from 1800 till today shows the latter's usage diverging noticeably from the former's around the era of 1940–1960, to becoming a much less popular a synonym for the former nowadays. The chart makes a lot of sense to me, at least superficially; the 1950s–1960s was an era where college attendance and job mobility were first greatly expanded and democratized, and where a lot of young adults who might have grown up to work on the family farm in older times instead found white-collar, professional work. As pail in literature is strongly associated in my mind with farming contexts, it makes sense to me that authors would have limited their use of pail in that era given its more limited relevance towards their target audience. If a word doesn't quite have a "regular" currency, obviously there will be fewer opportunities for it to make its way into slang usage.