Which sentence would you normally use as a speaker of AmE or BrE? Thank you :)!
1) The student scored 20 marks / points / grades on his exam / test.
2) The chart shows the grades / scores that the students achieved on their exams / tests.
3) The players scored 20 points and won the game.

Question

Which sentence would you normally use as a speaker of AmE or BrE? Thank you :)!
1) The student scored 20 marks / points / grades on his exam / test. 
2) The chart shows the grades / scores that the students achieved on their exams / tests.
3) The players scored 20 points and won the game.

Answer

I'll answer anyway, even if I don't specifically speak American or British (or Australian ;) English, although my English is slightly more British-based.
(a) I would use either points or marks. I don't think anyone uses 'scores grades'.
(b) exams and tests are different. Exams are more important/formal. You do an exam at the end of a course. You might do a test during the course, and it would not score as highly as an exam, if at all.
(c) grades and scores are different. Scores are marks out of some total, e.g. 15 out of 20, or 75%. Grades are normalised scores on a limited range, e.g. A-E (with our without +/-) or 1-5.
Your final one is fine.

Answer

AmE:
#1 Test results for normal classes are given in percentages. So we would say... "the student got an 80% on his history test" for example.
#2 Either is ok.
#3 Sure!

Answer

Absolutely not! I'd love to hear the preferred usage in Australian English!

Answer

Are you only interested in American and British?