An adhesive bandage, also called a sticking plaster (and also known by the genericized trademarks Band-Aid or Elastoplast) is a small dressing used for injuries not serious enough to require a full-size bandage. "Bandage" or "Band-Aid" is the common American English term, while "plaster" is the term in British English usage.
I actually read a really cool article on this. Band-Aid the brand has become so iconic that it's name has became "generic", so must people don't know that actually name is "Bandage" rather than by calling it by it's brand name "Band-Aid". Kleenex is having the same problem, you don't ask for a tissue? You usually ask for a Kleenex the brand because it has become the standard. Once a product company name has become to big it becomes a "Generic Trademark" and is no longer used for that just company. Examples of once trademarked words were "Kerosine, Phillips head screwdriver"