A の B has many meanings, depending on the relationship of
B of A,
B which belongs to A
- 彼の友達 his friend, a friend of his
- 私の車 my car
- 日本の都市 Japanese cities
B that is A,
B, being A (in this case, の is interchangeable with である)
- 友達のマイケル my friend Micheal
- トナカイのルドルフ Rudolph the reindeer
- 医者の乗客 a passenger who is a doctor
- ... and many others
Occasionally it can be hard to tell between 1. and 2. For example, 犯罪者の子供 may mean either "the criminal's child" (the child himself is not a criminal) or "a child who is a criminal", depending on the context.
In your case, the first definition is applied for 日本の学生 ("a student of Japan"), and the second definition is applied for 日本人の学生 ("a student who is a Japanese person"). They both mean the same thing, Japanese student(s).