Chrome makes it available to websites providing a PWA manifest, I believe. Firefox doesn't really have it on desktop yet, though there's a button and support for it on Android. Shortcuts on the desktop get added to where your computer would normally place these icons, be it your desktop, start menu, dock or apps folder.
You can sort-of replicate the behaviour by creating a shortcut to "chrome --app=https://www.example.com" for websites that don't offer it.
Firefox currently only has it as an experimental feature which you have to enable manually in about:config. I would have to say it still lacks a bit of polish. You can find it by searching for firefox ssb.
You can sort-of replicate the behaviour by creating a shortcut to "chrome --app=https://www.example.com" for websites that don't offer it.