Scholarships in the US are offered on the basis of merit, need or other factors such as sports, ECA, diversity and so on. There are some universities or colleges that provide scholarships on achieving a certain SAT or GMAT/GRE scores (and even do not require an additional application). Some universities or colleges, however, require a separate application with an essay.
Graduate students can apply for Teaching or Research Assistantships. Generally, they need to submit applications separately. It is important that they contact their department or individual professors to see if there are any positions available.