Cloud computing relies on sharing hardware and software resources over a network rather than on local servers or personal devices.
Difference between Public vs. Private clouds
A public cloud is offered as a service via web applications/web services( usually over an Internet connection). Private cloud and internal cloud are deployed inside the firewall and managed by the user organization.
There is another type of cloud, hybrid cloud. A hybrid cloud environment consisting of multiple internal and/or external providers will be typical for most enterprises.