Cloud computing services compose of cloud computing models that offer services directed to specific group of people involved. These can be classified into four major categories:

Private
Public
Community
Hybrid

Let us now understand about each one of these services one by one.
Private: A private cloud computing service is designed to serve individual organizations. This service may be managed internally by the cloud computing service provider or by some other party existing outside and hosted externally. Private cloud is also known as corporate cloud as it comprise an architecture rendering services to a specific number of people behind a firewall. With advances in technology that is prevalent in distributed computing and virtualization it is possible for the service providers to cater to the individual needs of the clients within the corporate world.
Public:
A public cloud computing is all about a service that offers standard cloud computing to the user. In this model the service provider creates various resources that are available to the public at large. This resource includes storage facility and application accessibility to the public over internet. These services may be charged or free of cost depending on the service provider. This can also be a model that runs on pay-per-usage.
When it comes to Public cloud, these often fall in the category of mainstream cloud. These are often traditional computing. These are dynamically provisioned to facilitate the public at large with the benefits of cloud computing.
Community:
Community cloud runs on a sharing basis that is designed to serve a specified community. These might be beneficial for organizations or companies that are within same community, more line a member or a group. For example a community of IT organization can opt for Community cloud services. The benefit for opting for these services will enable in sharing industry updates, common concerns like jurisdiction, security or compliance. These can either be managed by a third-party provider or managed internally. The costs to these services are evenly distributed to the users who are connected via community cloud.
Hybrid:
As the name suggests a Hybrid cloud comprise a combination of two or more clouds. This includes public, community and private. This model is based on providing hybrid service to the clients. Often the service model is inclusive of the best qualities of each model. The unique entities of each cloud service model is bound together to serve as one unique model to the client. Thus the client is able to avail the benefit of multiple models that are deployed to serve as one under hybrid cloud computing model. The systems that are working to provide these services are uniquely inter-connected to enable programs and data exchange to and forth from one deployment to another
Hybrid cloud computing is all about giving the user access to various service models. This service is designed to serve the enterprises demanding the benefits of each model which is provided in one service model. This may help in minimizing overcapacity of resources and help in balancing of critical applications.