After the great development in information technology, cloud computing has become an urgent necessity, as this technology connects many network systems, whether public, private or hybrid, and thus it will provide great scalability in the basic infrastructure for all computing resources, as the most important service it provides is cloud storage, through which data of various types can be uploaded, downloaded, and retrieved. Cloud storage services are usually accessed via the Internet, where users subscribe to pay-per-use services. Sharing these cloud computing resources will also lead to the emergence of a set of security vulnerabilities, and therefore we will need a set of measures to protect against these cyber-attacks. These data protections in public and private clouds are the main obstacles that limit the use of the cloud. In this paper, a detailed comparison was made about public and private cloud storage and the capabilities provided by each type in addition to the advantages and disadvantages. The study concluded that the private cloud will be widely used compared to the public cloud because it achieves almost the same capabilities of the public cloud with some differences between them in the security field, which in turn will lead us to develop and renew the security measures that must be taken to achieve data preservation.