They are different things and are not interchangeable in most cases.
-
IaaS: (Infrastructure as a service) You hire a virtual machine. You configure it as you want and you are responsible for it to work, to update it, etc. It is the most powerful of the forms of cloud computing because it gives you the freedom to do what you want on the machine.
-
PaaS: (Platform as a service) You hire a basic software (for example a web server). Only deploy (deploy) the application and others are responsible for the hardware and operating system. It is a not so powerful but more practical way for some solutions.
-
SaaS: (Software as a service) You hire a CLOSED service. (for example, JIRA). You only use the service, you can not add components (usually).
In short, there is not much chance to choose, in general, except between IaaS and PaaS since it is a web service, you should weigh costs + benefits - limitations.
Greetings.