The Chinese middle school is the equivalent of the American high school or UK secondary school. Like the American school, it's often divided into junior and senior sections.
If you are keen to work with children, younger middle school teaching is probably your better option. Your students should be old enough to get down to some serious work without needing 5 minute singing breaks all the time, but young enough to retain a certain enthusiasm for learning.
You'll hear people tell you that Chinese children mature more slowly than those in the west, which is fair comment. They're expected to make fewer of their own decisions and regarded as children almost until they leave home, without ever going through a 'young adult' stage.
This is probably most apparent in senior middle school and first year university students - instruction to choose a partner of the opposite sex could well result in the class forming two embarrassed single-sex groups, and uttering such risque words as 'kiss' could result in a terminal fit of the giggles.
Overall, this can be a very rewarding age-group to teach - there's a willingness to work hard that often leaves teachers used to western teenagers speechless (unless you count 'but . . . but . . . they're pleasant' as speech) and the Chinese seem to suffer much less from the sullen 'I'm not going to enjoy anything, and you can't make me' stage so beloved of western parents and teachers.
On the minus side the Chinese education system is not yet geared up to producing independent creative thinking, and questions like 'what do you think' are often met with polite pauses while the students wait to be told what they think. That could be said to be true right through the system, but I think it might be most noticable in the middle years, between the effusiveness of youth and the freedom of the university years.
Things are changing though. I've seen TV adverts on children's telly recently (ahem) telling kids that they should be asking as many questions in class as possible, and it was the teachers job to answer any and every question. Seems elementary stuff to us, but ground-breaking in a culture where Confucian respect for authority and a concept of the teacher as knowledge-giver and student as note-taker is the norm.