This is my first time using the Nxt wallet. I first downloaded and installed it from
http://nxtra.org/nxt-wallet/ (Mac version). Upon first installing the wallet it selected a randomly generated 12-word passphrase for me and gave me an account ID. I closed the wallet and then reopened it. I entered a different passphrase than the one initially given to me to see if the wallet would still give me access. The wallet gave me access to the dashboard but I observed a different account ID than the one given to me when given the randomly generated 12-word passphrase. Is this normal? Why do I get access to the dashboard and see a different account ID when entering an incorrect passphrase? I guess this stresses the importance of never losing you passphrase; otherwise you have no way of accessing the assets tied to a particular account ID ... I think.

Yes, the passphrase defines the account (brain wallet). If you enter a different phrase, you open a different account.
So... never lose it!
