When to use stubs and mocks?

I've this confusion all the time. If I write a code which uses fake code to assert some operation, how do i trust my real implementation when it is started really using the real objects instead of fake ones.

For example, I've this code --

    [Test]
    public void CanCreateContactsWithData()
    {
        using(ISession session = factory.OpenSession())
        using (ITransaction trans = session.BeginTransaction())
        {
            _contactId = (long) session.Save(contact);
            trans.Commit();
        }

        Assert.AreNotEqual(0, _contactId);
    }

This code tests the implementation of a "contact" object whether that gets saved into database or not. If i happened to use a stub instead of a real database connection, do I need to have separate test for storing it in database? And, do you guys call that as integration testing?

Answers are sincerely appreciated.