As a Kiwi student, I'd call them my "year level" or "fifth form" or "year eleven"
Having worked in a high school, another name is "cohort" but that is specific to the teaching profession and wouldn't be used by the students themselves. The idea of a cohort covers everyone who started in the lowest year together, and those who joined the group as all these students moved up the year levels together.
Sometimes students might be delayed a year in a subject, or some get to jump a year, and they're still in the same cohort even if some of their work is at another year level.
In other words, a cohort is a loose grouping of students with similar social-developmental progress.
If you're looking at the idea of "parallel" as the core, then another school-jargon word would be "stream"
Imagine a hypothetical school with three subjects. A mandatory Mathematics subject,and students who can pick their other class subject. Everyone HAS to do maths, but half choose to do French and half choose Computers.
This means twice as many maths class teaching slots are needed. So there is a "French stream" and a "Computers stream" and that dictates which Maths class you're in.
In theory both streams are doing the same Maths contents, just at different times which matches your "parallel" point.