Many Americans do not recognize any races between black and white. The terms mulatto and quadroon have fallen out of use. If a person has a grandparent or great-grandparent who was black, and does not look visibly white, then most Americans will consider that person black. Some Americans will consider someone black if they have any black ancestry despite their appearance. You might hear an American say "I knew her for years before I found out she was black" on discovering that someone had a black grandparent.
In contrast, Brazilians recognize many different races between 'black' and 'white' and only people with the darkest shade of skin will be considered 'black'. A Brazilian may easily consider themself white where Americans would consider them black.