As the title says^^ I think 生徒 is for elementary school, what about the other two？
Students are 学生 for most of their educational life:
I would always pass myself off as はかせかていのメンバー (member of the doctorate course). I was never corrected on this.
The other two act as group descriptors, rather than something a student would refer itself as:
According to Japanese animated television series, Japanese spend what is called their life in school and then transform into a rigid plant-like lifeform. Hence there are a lot of other terms describing that growth phase, such as:
Did you look this up in a dictionary? Even WWWJDIC has
which is quite accurate I'd say. 生徒 is pupil, not just for elementary school. If you want to be more specific about the level, there are
I think 生徒 is for elementary school>>残念ながら、本来は違うんです・・・^^;
"I think 生徒 is for elementary school"--I'm sorry, but I don't think this is right.
As established by the Ministry of Education,
So strictly speaking, 高校生 and 中学生 are not 学生; and 小学生 are not 生徒.
In Japan, it is not uncommon in everyday conversations that 高校生 are called 学生, and there are many people who use 生徒 for 小学生. (But of course, 中学・高校 teachers don't say うちの学生, they say うちの生徒; and 小学 teachers don't say うちの生徒, they say うちの児童.) As for things like newspapers, we would expect the words to be correctly used.
Also, people who are under instruction, as opposed to providing instruction, are frequently called 生徒. For example, the phrase "Our calligraphy class student(s)" is more naturally realised as "うちの書道教室の生徒" than "うちの書道教室の児童".