Google's login sequence

If there's one thing about Google that drives me potty, it's the variety of username/password possibilities for something that should be som simple.
I have an AdSense account. I have an AdWords account. I have a Google Analytics account. I even, somewhere in the mists of time, have a GMail account. But do they all use the same username and password? Do they heck. Only on Google could you get a response like this on trying to log in:

Welcome! You are signed in to Google Accounts under the email ivan@ivanpope.com and your Google Account password, but this is not a valid AdWords login. If you are an AdWords advertiser, try signing in using your AdWords email and password. Or, sign up for AdWords.

Uh? I'm logged in - BUT I'M NOT LOGGED IN. Try Again, dimwit.