publish_post And Posts Scheduled In The Future

I want to do a certain action when the post is published, but I don’t want it to be done when I save it. This is very important considering posts that are scheduled in the future.

So, the question is: save_post works whenever I hit “save” or “publish” right? That means: even if I schedule the post to be published in the future, the “save_post” action would be fired right away?

If I used “publish_post”, would that change it to only fire at the time the post “goes online”?