We haven't heard of Private PaaS or Public PaaS (or hybrid!) but the industry is clearly moving in multiple directions here if you observed App Engine, Azure, Force.com, Heroku, Engine Yard, ActiveState, AppFog, Tier 3, Uhuru Software, PaaS.io or CloudFoundry.com.
VMware is clearly pitching for private PaaS within enterprises to deploy internal applications. This would enterprises to have a common PaaS platform that results in 'standardization' and 'governance'. While the productivity boost is questionable since any PaaS would need a mindset change in the developer community and PaaS enforces thinking in one-way.
It is interesting to see so many new PaaS platforms (such as AppFog) as new-entrants in the market (some based on CloudFoundry), and others with the message of running PaaS across infrastructure providers. If I am anyway going to be on PaaS - why worry about IaaS flexibility - I am locked in at the usage layer itself.
