A の B has many meanings, depending on the relationship of A and B:
- (possession/affiliation/belonging)
B of A, A's B, 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
- (state/description/apposition)
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).
AのBcould always be translated asB of Amechanically, then 日本人の学生 should mean "student of Japanese people", which makes little sense to me. – naruto Nov 14 '16 at 13:06