grammar - What's the difference between 日本人の学生 and 日本の学生 ?

I am beginner to Japanese language. I am using Genki as textbook. I came across this sentence in one of the exercises:

あなたの学校に日本人の学生がいますか。

Why is it 日本人の学生 here and not 日本の学生 ? Wouldn't 日本の学生 (Student of Japan/ Japanese student) make more sense than 日本人の学生 (Japanese person student) ?

Am I interpreting it wrong ?

Answer

A の B has many meanings, depending on the relationship of A and B:

1. (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
   
   
   
   


2. (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
   
   
   
   
   


3. ... 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).