A post from Stefan Reid teases a full report from Forrester laying out a more comprehensive cloud taxonomy. I continue to believe that you can't successfully make decisions about a cloud strategy unless you have a good grasp of what is meant by cloud, and what types of cloud might influence your decision strategy.
This graphic suggests you should consider private clouds to be primarily a visualization story.
I have no relationship to Forrester but if understanding cloud taxonomy is important to you, this may be a useful report. Link: http://blogs.forrester.com/stefan_ried/10-07-06-forresters_cloud_computing_taxonomy