The difference is visible from the very name of the services. A web app is a combination of technologies such as server-side script and client-side script. A web browser is sometimes called a “thin client” and it is fetching the components on the backend to provide the functionality of bespoke (custom) web app development. Anyone knows Facebook, Flipkart, and Twitter. All of them are web apps.
SaaS is nothing but an evolved web app. It can access data on the internet, but not always is dependent on the web browser to operate. They are easy to customize and operate. However, they provide smooth integration with the back-end. The most common SaaS app is Dropbox.