D7 CKEditor missing buttons
Hugronaphor's comment helped me find a solution that worked for me... I'm just going to explain it clearly.


Browse to /admin/config/content/ckeditor 
Edit the CKEditor GLOBAL Profile
Under the "Advanced Settings", change the "Path to CKEditor"


What you enter here will depend on whether you have downloaded and installed the full package (as described in my initial question) and where you have installed it, or whether you want to use the CDN.
The instructions given below the text box are quite clear, but much like anything, it's just knowing where to look !

Because I'd already installed the full package and installed it to "modules/ckeditor/ckeditor" it means instead of using the CDN, I entered "%m/ckeditor" which made it work perfectly.

If I'd installed the full package to "/sites/all/libraries/ckeditor" I would have entered "%l/ckeditor"

...and if I wanted to use the CDN version, I would have entered "//cdn.ckeditor.com/4.4.3/full-all"  Although, I assume this version number will possibly change in the future