
Cloud computing is a way to use (and also deliver) computing resources (for a formal definition see The NIST Definition of Cloud Computing).
For this reason there are different types of cloud based on which type of “computing” resources are provided. Mainly there are three big silos:
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Infrastructure as a service (IaaS): usually it provides VMs a virtual datacenters resources (like storage and networking), and also the infrastucture need to manage them. An example of this kind of cloud is Amazon EC2.
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Platform as a service (PaaS): in this case a developer platform is provided that usually include OS, libraries, programming language execution environment, and all that could be useful to provide multi-tiers application (included usually database, presentations servers, …). An example of this kind of cloud is Microsoft Azure.
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Software as a service (SaaS): in the case a single application or service is provided (or a set of them). An example of this kind of cloud is Microsoft Office 365 or Google Apps.