ITunes password problem

I attempted to purchase an iBook on my iPad but when I entered my iTunes password, the message stated that "The password is invalid". I attempted it a few more times and got the same message. My Apple and iTunes ID and password were exactly the same until I recently changed my Apple ID to my Gmail address; but my iTunes ID has not changed. The password for both accounts is the same. How can I change my iTunes ID to the new Apple email ID? Could this lack of identical ID's be the reason that my iTunes password is coming up "invalid"? Is there a way to have totally different ID's and passwords for iTunes and Apple accounts or do they have to coincide? Is there any way to change my iTunes ID to my email address? Please respond ASAP. Thank you.
PS: I also tried purchasing music on my computer and got the same result.