No you don't. With Facebook, you hit the button, Facebook asks if you want to link your account - that's another button - and from then on it's a one-button login. Users are so used to the Facebook login button that you don't have to explain it, you just put it there. (I'm pretty sure the button says log in, too.)
And Facebook doesn't ask you for your user name or password - you can't phish if the site doesn't ask it to begin with. It just matches your cookies. If you haven't logged in yet, then you need to go to Facebook and log in first. But most people are logged in constantly, so it works out.
Yes. But that's where the issue of popularity and singularity pops up.
For Facebook, there's a huge userbase that's already there, and already cookie'd up. Because Facebook has such a huge brand name, it can stand alone and work pretty well.
OpenID, first off, has a DISadvantage in how open it is. No single large button will work. (I love the idea of Clickpass, I think that it has a chance to work, but that means yet another branch of the original OpenID concept.) You need either one single field to log in from, or you need multiple buttons, one per service.
From there it's a matter of individual service popularity. And here's from my experience only, so I could be speaking alone, but the services I used didn't remember me and I had to log in each time. I used ClaimID, MyOpenID, and AIM. Same problems with each. And I used OpenID to AVOID multiple logins. Even when I'd logged in for one site, the second one meant entering my log in again, then going to a second page to verify access. That means the log-in process is longer than just using a separate ID for the site. Registration moved slower, too, because first I had to log in, then I had to grant access, then I had to pick a user name - half as many page loads as even registering with a site using email verification. (Sites that used OpenID AND email verification were the last straw.)
So... conceptually, yes. Exact same process. The difference is that with Facebook I need two clicks to log in, no keyboard, and two clicks is fair to me. The same as theoretically entering a user name and password. And registration is faster, and it keeps all my identities together. So Facebook, by being a faceless corporate entity, has a usability edge, and for the majority of users (I'm not a fan of either, mind you), usability is all that matters.
And Facebook doesn't ask you for your user name or password - you can't phish if the site doesn't ask it to begin with. It just matches your cookies. If you haven't logged in yet, then you need to go to Facebook and log in first. But most people are logged in constantly, so it works out.