When your hosting account was based around a single server, you had the choice of either sharing the machine with other accounts (a shared server) or running an individual machine specifically for your site (a dedicated server). With cloud hosting you have a similar choice to make.
Shared Hosting
Shared Hosting also known as Public Cloud Hosting. It is similar to a shared server where a collection of networked machines holds the data for several sites.
The hardware is shared between several virtualized accounts, and so the cost of the resource is shared. Unlike traditional shared hosting, however, the virtual server’s resources are ring-fenced. You don't share disk space, processing power, or anything else with any other account – you simply share rack space in the data centres. In effect you get all the benefits of shared hosting, with none of the downsides.
Private Hosting
On the other hand, a private cloud (private cloud hosting) does not share its infrastructure with any other accounts or sites. This obviously comes with a higher cost but offers greater security and control.
Server resources are ring fenced within private clouds, meaning that you don't have to share hardware. The entire virtualized resource sits behind your own firewall.