Learn English – the difference between ‘despair’ and ‘hopeless’

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.

In short: puberty is a period of physical transition, adolescence is about a psychological and social transition.

Puberty is the process of physical changes by which adolescents reach sexual maturity, i.e. become capable of reproduction. Puberty refers to the bodily changes, while adolescence is the period of psychological and social transition between childhood and adulthood. (sources: Wikipedia and New Oxford American Dictionary).

In nonspecialized discussion and writing, the meanings tend to get blurred, and puberty can be used to refer to the period during which the changes happen, getting a meaning closer to adolescence. Adolescence still encompasses a typically larger period of time, however: puberty is over when the young individual's body has fully transformed, while it takes some more time for him or her to be recognized as an adult. Criteria for the latter are somewhat arbitrary, the typical example being “having reached the age of majority or being emancipated” (the age of majority depending on the country of residence). Some people even talk of 20-something adolescents to refer to people who have not yet reached an autonomous state of living, while being of full legal age.

As a side note, adolescence has a related noun (adolescent) and adjective (also adolescent), while puberty has a related noun (pubescent) and three adjectives (pubescent, pubertal, and sometimes puberal). It also has a synonym, "pubescence."