Fair enough, we don't use the term semester here in the UK. I assumed it meant next school year, not term. The dialogue really is a language barrier
Semester and term are kind of the same thing as they refer to a particular block of time within the academic year. The main difference, I believe, is that "semester" refers to each full half of the academic year (the Fall semester that ends before Christmas and the Spring semester than runs to the end of the school year), and "term" refers to smaller chunks within the school year, like how the first half up to Christmas is divided into 1st term, half-term, and then 2nd term.
Even with that, "term" seems to generally be used more formally by teachers, news reporters, and politicians, because when I was in school we students would more typically use "year" as a double meaning which is what Sage would seem to be doing here.
Yeah, Sage probably should have said, "in the spring," or "next semester" instead of next year. That's how I've heard people in the U.S. say it (but I never really took note of the specific in-game location for B&R). I recently replayed chapter 5 and Sage herself says that she is a senior during her guitar lesson in the grass with MC. I don't have a screenshot of it though.
It could be a difference in the cultural way of speaking because I know from my own experience that students here in the UK generally use "year" to mean both the school year and calendar year as in the phrase, "this is my final year so I'll be graduating next year". Perhaps the Swedes have a similar parlance to those in the UK, hence why DPC wrote it that way.