I've seen this not documented anywhere, so I'm just writing this down here. You'll need to know this so your .desktop file can set your wm/taskbar icon correctly.
The .desktop file that Nightly installs (when it asks you if you want it to become your default browser) isn't aware of Nightly, and incorrectly sets StartupWMClass to firefox, thus Nightly will get a generic icon.
Good on them. Snap is a plague.