Don't run from “the cloud” – you can't – it's all the latest buzz and, it's probably where the majority of your personal and professional data is already stored.
Now we're hearing about Public vs. Private Cloud implementations.
Being a Technologist with a lot of focus in this Cloud Computing Sector, I have coined some “elevator pitches” that explain the difference between the two.
Public Cloud: Also known as the “shared cloud,” this model involves an environment where a provider offers shared access to services through the Internet. Those services usually include compute, storage, networking, and secure connectivity.
Private Cloud: Private or internal clouds reproduce the best characteristics of the public cloud without the exposure to other users. The private cloud can be deployed in a number of configurations, but to-date, we're typically seeing it as a provider offering an organization dedicated servers, dedicated networking and either dedicated or centralized storage options (storage area network).
Look at this infographic, provided by wikibon, that visually shows some common differentiators of the two offerings.