OK here goes

linux (/boot/vmlinuz)
This one is easy. You can just call it a "Normal Boot". You probably know what that does

failsafe(/boot/vmlinuz)
This one is there in case an update or a configuration change causes an error which prevents your system from starting properly. It boots into a VERY MINIMAL environment so that (advanced users) can diagnose and repair the problem which is causing the failure to start. This minimal environment only has a "command shell" (no system services are started or external drivers loaded and certainly no desktop will appear!) I guess it's kind of equivalent to the Recovery Console on Windows (only MUCH more powerful of course!). So I would call this one "Recovery Console" or "Repair Console"
linux-nonfb(/boot/vmlinuz)
This one is more interesting because it won't appear on a Graphical Boot Menu!. Nonfb is short for "no frame buffer driver". The Frame Buffer driver (FB) is s special driver that can talk to the graphics card for displaying graphics. In the early days of this driver there were problems using it with some graphics cards, so an option was provided to disable it (not really necessary these days). So the reason you won't see it on the Graphical Boot Menu is because the Graphical Boot Menu is produced using the FB driver. So if you can see the menu you know it's working

(You can hit Escape which will drop you to a "text" menu where you will see all 3 options.)
So I'm not sure what you would call this one

Hope that helps
Terry