It was strange to see this word here... Swedish and Hungarian has next to nothing in common (vocabulary-wise), but this word is the same - though in Hungarian it is old-fashioned and rarely used. So I looked up the etymology, since with English it is a false friend. Thing is, both meanings came from french (surprisingly), from the same root (meaning 'bring back'), but in English it became a 'close, harmonious relationship', while in Swedish and Hungarian it became a report, that has very little to do with emotions. So, the conclusion is that the English are more emotional than the Swedes and the Hungarians. :-P
I'm not sure, since the Swedish education system works differently than the American one. Perhaps skolrapport or betygsrapport but it's hard to find a fitting translation.
So how do you know if the person has understood what was taught to them over the course of the year ?
Swedish secondary education lasts three years and is based on courses, such as Matematik 1, 2, 3 etc or Engelska 1, 2 and so on. When a course is finished, you get a grade on that course. After each year, you will have finished some courses and accordingly receive a grade in that particular course.
In most courses (but not all) there is also a nationellt prov (national test) at the end, which is the same for everyone and written simultaneously throughout the country. They're not exams as such, but they are meant to normalize the grading. A student's performance over the course of the year is still an important part of grading their performance. For more information, I'm sure there are googleable resources out there.