I think there are several threads in the archive (Suche in allen Foren) that discuss all these senses. One of them would really be a better place to revive the discussion than here in Wrong Entry.
As far as I know, a bank holiday in the UK is usually a single day, often one that creates a long weekend. In the US we often call them Monday holidays (because most are observed on Mondays) or federal holidays. They're official or public holidays, when all federal government buildings, including post offices, and most banks and schools are closed, but not all private businesses, and usually not stores or restaurants.
The more general word holiday, in contrast, can be any single day that's celebrated in a particular tradition. Christmas, New Year's, Valentine's Day, St. Patrick's Day, Easter, Eid al-Fitr (sp?), Yom Kippur, Independence Day, Guy Fawkes Day, Canada Day, Cinco de Mayo, Reformationstag, Mother's Day, Father's Day ... Sometimes those are also federal (AE) / bank (BE) holidays, but sometimes they're not.
For several days or weeks together, it's usually holidays in the plural in BE, but in AE it's often vacation in the singular, and holidays only in certain contexts.