Infrastructure-as-a-Service is a step away from on-premise hardware and storage. Instead of having to own and maintain servers, it's handled for you on a virtual machine securely hosted in the cloud.
The IaaS model is great for companies who want full control of their systems but don't want the burden or cost of maintaining physical server and network equipment.
Platform-as-a-Service is a type of cloud computing offering in which a service provider delivers a platform to clients. This enables them to develop, run, and manage business applications without the need to build and maintain the infrastructure such software development processes typically require.
PaaS is ideal for developers who may need to quickly deploy SQL servers. Or for those who simply want to bypass the headache of having to build-out a server and install everything needed to develop, run, or test their applications.
Software-as-a-Service is based entirely on the Internet, and it is an approach to software distribution by which software providers host a combination of servers, databases, and code to create applications that can be accessed by users from connected devices.
SaaS provides the highest level (least amount of management required) for businesses today. SaaS is a solution that encompasses the virtual hardware, the platform required to run apps in the back-end, and the productivity software. Ex: Exchange, SharePoint, OneDrive, etc.