The CKeditor module gives you much more detailed control over the editor windows, user level permissions and the available buttons for each of them. The WSYIWYG API allows you to use the basic on / off editor window for text fields throughout the site. Button profiles are based on input types (filtered and full HTML). The advantages of the API module are that it is not limited to one editor (there are 10 or so) and is very easy to configure.
The Ckeditor module is harder to configure and, of course, not for most implementations, but it is very nice to have this module if you need this level of control.
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