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PaaS - will offer Platforms - in simple Operating Systems where other softwares and applications are run locally and virtually
SaaS - will offer Softwares and Applications - in simple Softwares where you can access them via web browser or VPN connections.
SaaS is software that is deployed on a hosted service and can be accessed globally over the internet through a browser. The user only interacts with the SOFTWARE.
PaaS is best understood in the context of an environment where a developer is able to create solutions using the development tools that are provided on the PLATFORM.
Essentially, SaaS is a cloud computing model that is offered by a vendor providing the equivalent of the software that you can buy off the shelf, while the PaaS model allows customers to enter and retrieve data, perform actions, customize the platform involved and get results.