Harp actually is a static generator (didn't think it was, never used before).

And yes, Grav and Cockpit are self-hosted flat-file CMS, but now that you ask makes me confused. I was under the impression that Lektor was similar where you have a flat-file CMS and whenever a change is made, the static files are created.

My second guess is that this actually a CMS that exists locally and deploys static files when a change is made?

Lektor is a static site generator: it generates a "compiled" version of the site that is uploaded to a simple web server, without any server-side scripts running. If you want to edit something, you run it locally, make your changes, generate new files and copy those to the web server.

The key addition is that there is a nice UI for adding content in the system running locally, so it can be used by less technical users that might not feel comfortable with writing in text files with special tags/metadata, as traditional static generators require.