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Not really, is a offline chess page not an app? It seems like it would be closer to an app.

What does this hypothetical chess page do? And how’s does it do it if it is static?

You misunderstand the meaning of static web pages. Here's a short explanation of the terms: https://developer.mozilla.org/en-US/docs/Learn_web_developme...

It uses javascript. Still a static file. Lets you play chess

Don’t you update the DOM to render the pieces as they’re moved?

A static website is one that doesn’t have an associated backend API server, just serves as one or more self contained file assets.

The files you serve to the browser are static, not the contents of the page itself

Updating the dom can happen with only individual assets, so it’s a static site

when someone describes a static site/app they generally mean there is no backend. not that the frontend is a static image

for example you can service static sites from S3 that have HTML/CSS/JS but no API or DB