I don't understand. You've got to save the edited result in a file somehow. What format do you use?

The file as it comes out of the camera, so-called raw, is a family of formats. Usually such files are kept untouched and any edits are saved in a lightweight settings file (in the format of your editing app) alongside the original.

Is that like how javascript was named so as to imply a connection with java, in spite of there being none?

JPEG is the ur-example of lossy compression. JPEG Lossless can't have any connection with that.

I'm not even really a hobbyist photographer anymore, but when I was, the full lossless edit was a .psd and that was generally exported to (high quality) jpg for distribution. I have folders full of carefully curated raws. For the relatively few that were ever edited they have an accompanying psd. The jpgs are ephemeral and don't get saved long term.