There are two types,
1. Community Cloud
Community cloud shares infrastructure between several organizations from a specific community with common concerns (security, compliance, jurisdiction, etc.), whether managed internally or by a third-party and hosted internally or externally. The costs are spread over fewer users than a public cloud (but more than that of a private) to realize its cost saving potential.
2. Public Cloud
A public cloud is established where several organizations have similar requirements and seek to share infrastructure so as to realize some of the benefits of cloud computing. The costs are spread over more users than a shared cloud (but more than a single tenant). This option offers a higher level of privacy, security, and/or policy compliance. In addition, it can be economically attractive as the resources (storage, workstations) utilized and shared in the community are already exploited.