When authors say they are working on their 2nd draft, does that mean they completely started over or they are doing revisions on their first?

That depends on the author! When I say I’m working on a second draft, what I mean is that I wrote the first draft, turned it in to my editor, and now I am implementing the notes she gave me. So basically my second draft means I’m editing. A lot of authors prefer to gut their entire manuscript and start over, using the first draft for notes mostly. But every writer is different.