there's a FB live stream and facebook comments, I donn really understand what's the diff, and which one of them is better for my website, I have daily half hour live streaming can I use both into my website?
Do you mean this plugin: http://developers.facebook.com/docs/reference/plugins/live-stream/ ?
I've used it before, and while it's flexible enough, it does have some serious limitations. It only displays a fixed number of comments at a time, and you have no control over it. It's ten or twenty. And once a comment has been "bumped" off the view, it's practically impossible to find. I believe the comments still exist, but there's no practical way to view the old comments that I've seen. So if you want to archive comments in a live stream, or otherwise get retrospective access to them, live stream is useless.
Another real limitation is removing comments from a live stream. it's impossible to do on a comment-by-comment basis. Let's say a user accidentally double posts in your live stream. In a well-built component, an admin could simply delete one of these.
In Live Stream, however, the only way you can cause a user's comment to disappear, is to ban them from the page associated with the live stream, at which point all their comments disappear. This is incredibly frustrating. From what I've read, it was once possible to remove individual comments from a live stream, but Facebook removed this functionality.
Bearing that in mind, if you're ok with having a chatbox on the site that is very throwaway, and you don't care about having fine control over the comments, Live Stream is easy to use, for what limited use it has.
If you want to have any amount of control over what appears, use comments instead.