What's the difference between enterprise cloud and private cloud?

"Organizations going down the private cloud path have some tough decisions to make.  (Why Private Clouds Are a Catch-22 for Buyers, GigaOM)

This title question appeared on Quora . The first Catch-22 is to define what a private cloud is Here are some opinions, all valid.

"A private cloud is behind a firewall - the likelihood is therefore that it is being operated by an organization's own data center".  

"The term 'private cloud' as it's used now seems to miss the entire point of cloud computing."

" Enterprise Cloud is a euphemism that a small number of marketers and vendors will use to describe on premise blend of IaaS & SaaS. It is simply a private cloud plan and simple

"The private cloud means user own the resource privately and use the resource privately"

 "Private Cloud ... is a marketing term being applied to private IT resources that are organized, orchestrated, managed, deployed, and used in a service oriented model"

 The main reason any organization wants a cloud is to make more money than it does now. A bunch of computers, no matter how well orchestrated are not a cloud.  Here is my take on private clouds

"There is no difference between a private cloud and a customer using a public cloud. If you use your own physical servers, the creation of a cloud with elasticity & billing of resources is very complex, The private cloud software really relegates the CIO to the same headaches of running a data center today.

One can build exactly the same private cloud using software servers. IaaS providers like CloudSugma - give customers root access, and the option to install whatever software they need to mount the application and services, the same as for physical servers. You select your own security and firewall, or select it from the 3rd parties on CloudSigma. The software offered as PaaS is from 3rd parties only and it is optional. CloudSigma's customers select which 3rd party PaaS they like from CloudSigma site (jclouds, enStratuss, AppFrist and so on), or they can select none.

AWS slogan is "we do the heavy lifting for you'. This is true, the intention is to remove all complexity and so one can have it's own private cloud on Amazon public cloud. CloudSigma goes a step further, and gives customers the ability to create a cloud in a day, using the same experience curve familiar from having a bare physical server; load the OS, load the middle ware, use CloudSigma billing and ask your customers to use your services with a credit card.

Servers as software are better: cheaper, faster, more fault-tolerant, and more secure than traditional servers.  The shift from private to public cloud is related to hardware replacement cycle. So what we call today private clouds, will become simply a readily available service from public cloud. The owners of private clouds will have the same exclusive privileges they have on their own premises"

So why not build the private clouds using the public clouds resources?