A website is defined by its content, while a web application is defined by its interaction with the user. That is, a website can plausibly consist of a static content repository that’s dealt out to all visitors, while a web application depends on interaction and requires programmatic user input and data processing.
For example, a news site would be a “website”, but a spreadsheet or a collaborative calendar would be web “applications”. The news site shows essentially the same information to all visitors, while the calendar processes individual data.
Practically, most websites with quickly changing content will also rely on a sophisticated programmatic (and/or database) backend, but at least in principle they’re only defined by their output. The web application on the other hand is essentially a program that runs remotely, and it depends fundamentally on a processing and a data storage backend.
They are not entirely exclusive. A university website likely gives information such as location, tuition rates, programs available, etc; it will likely have web applications that allow teachers to manage grades and course materials, applications for students to register for and withdraw from courses, etc.