1) I don't have any books
2) I don't have any book
How are they different ?
The first sentence is correct. The second is not.
***** NOT A TEACHER *****
(1) I think the difference is:
I am a very poor person. At home, I don't have any books. (= I have
no books.) Would you please give me a few?
(2) Tom: Where is my math book? I know that you took it without
my permission. Give it back to me right now!!!
Martha: What book (are you talking about). I don't have any book (that
belongs to you). And I resent your accusing me of taking it.