In the United States, there is no standard. The system of grading courses differs from school to school. Within a school, the system for grading a quiz or homework assignment differs from teacher to teacher.
In the United States, the only rule is to do whatever your particular school or teacher does.
The most general term is "a grade."
Numeric grades may be call "a score."
Numeric grades may be measured in "points."
Numeric grades may be expressed as a percentage of a perfect score. If a quiz has five questions, and questions 1-4 are worth one point each and question 5 is worth five points, and you get all but #3 correct, you might say:
"I scored 9 out of 10 points."
"My test score was 9/10."
"I got 90%."
Letter grades are common--and totally insane. A common pattern is "A, B, C, D, F." F stands for "failing" and is not part of the alphabetical sequence. Letter grades may allow + signs to mean slightly better performance: "A+, A, B+, B, C+, C, D+, D, F." They may also allow minus signs: "A+, A, A-, B+, B, B-..."
Some colleges use a numeric form in which the highest possible value is 4. My own college, MIT, for some reason, chose to use 5. So a Harvard student with a "four-oh average" (4.0) has a perfect record, while at MIT "four-oh" is only good, while perfection is "five-oh."