Americans use the brand names for things such as using 'band-aid' which I would think of as a type of plaster.
A "plaster"? OK, there's yet *another* word I wouldn't use to mean what you use it to mean. Plaster to me is a white powder that you mix with water to make a paste. You might use the resulting paste to fix a hole in a wall, but you wouldn't put it on a cut.
To me, the generic for band-aid is bandage.
Edited to add: But you are right. I call bandages "band-aids", regardless of the brand.
