Difference between 持っている and ある

持っている - to hold, carry or have
ある - something is there or present.

Main difference between 持っている and ある: (when used as "have")
持っている is transitive (it can take an object)
ある is intransitive (it cannot take an object, the object being "had" is the subject).

Example:
ぼくは本がある.
I have a book (using subject + ga + aru).

ぼくが本を持っている.
I have a book (using object + wo + motte iru).

If you want to specify that the book is not with you, you're going to have to add another part to the sentence saying so. Like for example:
本がある。たぶんかばんにあるでしょう。
I have a book with me, maybe in my bookbag.



You can say 本がある or 本を持っている for saying you have a book but not with you.
You can only say 本を持っている if you have a book and you are currently carrying it.

Usually though, in conversation, you don't just say this. I can't remember anytime when someone has asked me, "Do you have the book?" without just wanting a simple "Yes, I have it with me right now" or "No, but I do own it" and it's all obvious by context.

Teacher: (You need a book for class) Do you have the book?
Me: Yes, it's right here.
Me: No, it's at home.

You wouldn't say, "Yep, I have it" when you don't have it currently with you without clarifying. Like "Yeah, I have it, but now with me right now."
Same for Japanese.


Source: http://answers.yahoo.com/question/index?qid=20081203203119AADtIoq