With a website, the idea is a visitor might only visit a single page. Under this model you want to ship as little JS as possible, and ensure that if the user just tries to read a blog post, the entire site isn't getting downloaded.
Contrast that with a webapp. I'm currently building a real estate investment calculator/dashboard and the mental model is diametrically different than building a website. Unlike a site, I want the entire app to be loaded upfront because the user is using the "entire" app, not just viewing a page.
The problem I see is when one is trying to design a "site" but uses the "app" model, or vice versa. Attempt to use an SSR framework like NextJS for an "app" and you are going to have a bad time, likewise try setting up a site like you would a webapp and you are going to have some pretty serious limitations.