I would like to know what is the difference between a SaaS and an API. I feel like it's somehow the same. So let's say I building a Rails or Flask api can I say that I'm buiding a Rails or Flask SaaS?
saas: Software as a Service (SaaS) is a software distribution model in which applications are hosted by a vendor or service provider and made available to customers over a network, typically the Internet.(source)
api: API stands for Application Programming Interface and it's simply a way to get information and pass information to trusted partners. Category. People & Blogs.(google)
A Software as a Service is a complete application that hosts/supports multiple users from a single code base. Gmail, Hotmail, Dropbox, Google Drive, Stackoverflow - pretty much anything you are using online and is also used by multiple people as a service.
An API is just a way for others to build on top of your existing application. An API doesn't need SaaS, and APIs have been around a lot longer than the Internet itself.
If you are building an API, it generally means you need others to build on some data you are exposing through the API, or extend an application for which you are creating an API. You may decide to host this API online simply for ease of use, and you may decide to host the resources online as well. Now your entire product API + resources + interface is an example of a software that is being distributed as a service.
However, you can perfectly use an API to create application that are completely offline. For example, you can create a new extension for Chrome or Firefox using the browser's API, but Chrome is not "SaaS".