What is the difference between wysiwyg module + ckeditor and ckeditor module? What is the difference between using the Wysiwyg module and the CKEditor - WYSIWYG HTML editor module? Are there benefits on using one over the other?
I've played with both recently and can offer some insight, at least for Drupal 7.

The Wysiwyg module lets you use any number of editors, such as CKEditor. It also integrates with the Media module if you use that. If you don't want to use CKEditor, but, say, TinyMCE, then you'll want to use Wysiwyg.

The CKEditor module is (obviously) just for CKEditor, and has more options specific to CKEditor. For example, you can change the skin CKEditor uses (Office 2003, Karma, etc). You can also set advanced CKEditor config options which you can't do with Wysiwig+CKEditor. It also integrates with some file browser modules like CKFinder. And I believe you can use the Media module with new versions of CKEditor.

One of the big reasons I went with the CKEditor module is that it doesn't strip out JavaScript. I couldn't find a way to get Wysiwyg+CKEditor to preserve JavaScript.