Are American class sizes really that big??

I’ve been lurking on this sub since I’m not an US teacher and I don’t have a lot of input on the problems that you guys have. Anyways I usually see a lot of posters stating that they teach “8th grade history” or “5th grade social studies” which got me wondering since where I teach (Estonia) it is very rare that a teacher only teaches one grade at a time. To give a little bit of context: here there are two core subjects (maths and mother tongue) which are tested and are taught 5 classes (45 min each) per week, rest of the subjects are taught 1–3 times per week depending on the school. The average amount of classes for a teacher per week is 21–24, which means if you are teaching a core subject you have at least 4 different sets of students and if it’s not a core subject it’s about 7 different sets of students. An average school has about 3 sets of students in a grade (around 70 students for ground school and 100 students for high school) which means that it is very unlikely for a teacher to teach only a single grade level. Usually teachers also stay with the grade level until they graduate which means that the teachers for a grade don’t change year-to-year unless someone leaves. How does the system work in the US? Do teachers only teach one grade level at a time and how big are the grades that this is a viable solution? How do students cope with getting a new teachers every year? How do teachers cope with having a new set of students each year and not being able to actually get to know them? Thanks in advance! Hope i haven’t misunderstood anything :)