I have seen sometimes HOSTS have 0.0.0.0 address or sometimes IP address.

I just dont understand the difference between these two and their benefits

Both are explained in the wiki:

http://en.wikipedia.org/wiki/0.0.0.0
http://en.wikipedia.org/wiki/IP_address

I hope the above links can clear your doubts up. If not, read them twice and then re-think your question in a way we can actually answer it.

What is the benefit hosting a service on 0.0.0.0 ? can you answer to this ?

0.0.0.0 means basically "no ip direction at all".

The "benefits" of that? Well, I guess that if you are asking that it is because you are in a very specific situation which I am not aware of.

I can only be imaginative and, in fact, imagine, that configuring a given network service to listen on a network interface which has an ip of 0.0.0.0, will allow you to run the service without actually giving it access to any network at all. But you already can do that with the loopback interface, which usually points to 127.0.0.1, and is aliased to "localhost".

It might have an use in a very specific circumstance, but I can't really be any more concrete without knowing what are we talking about.

It's like asking "what's the advantage of emptiness in the outer space?", well, it really depends on the task you have at hand.

I assume this means service is limited to this particular box only. Its just isolated . other machines in the same network can not access the service. am I right ?