Smart Author - It will show you yourself author box profile. But you need to login first. If you are in oggedout condition, so it will show author box from default user.
Static Author - It will show you author box profile from exact user. You can set the user ID on the widget settings
Post Author - It only works if you put it on single blog page. It will show author box profile from the Blog/Article Author. For example user "KaineLabs" publish an article. So, if you visit that article page, you will see KaineLabs Author Box.