It seems to me that "account creation code" is the more general term, encompassing both paid and free accounts, while "invitation code" is specific to free accounts.
Actually, here's a proposed rewrite of the FAQ, also incorporating leora's feedback from a few days ago:
LiveJournal relies on the community it creates to maintain an enjoyable journaling environment. In order to encourage healthy community growth, new free accounts must be sponsored by a present member of LiveJournal.
In order to join, you will need to obtain an account creation code. You may be able to obtain an invitation code from another user, allowing you to create a free account. They can generate their invitation code(s) by following the instructions in http://www.livejournal.com/support/faqbrowse.bml?faqid=142. On the Create Journal page (http://www.livejournal.com/create.bml), you will be asked to enter that code.
Alternatively, you can decide to pay for a new account. In this case, you will receive an account creation code once your payment is processed, rather than needing to get one from a friend. Prices for accounts start at $5 US. For more information about how to purchase an account, see http://www.livejournal.com/support/faqbrowse.bml?faqid=21. For more information about the benefits of paid accounts, see http://www.livejournal.com/support/faqbrowse.bml?faqid=131.
Once you have obtained an account creation code, see the following document to finish the creation process and start using your journal: http://www.livejournal.com/support/faqbrowse.bml?faqid=55.