Fast Boot in the BIOS is a setting that allows it to skip certain stages of POST.
Fast Startup is a form of hibernation that dumps the contents of the RAM onto the HDD/SSD and copies it back to the RAM on the next boot to speed up the initialization of Windows.
Be aware that Fast Boot can sometimes make it impossible to access the BIOS or boot menu via keyboard hotkeys. "I enabled Fast Boot and now I can't access the BIOS" is a common complaint. In this event, if you're using UEFI mode, you can initiate a restart to the BIOS from within Windows (8, 10).
I find that Fast Boot usually has a negligible effect on overall boot time, so I never bother enabling it. To get the fastest possible boot, you want to install Windows 10 in UEFI mode, with the BIOS set to UEFI and CSM disabled/secureboot enabled (assuming UEFI GOP GPU etc.).
There's no point disabling hibernation if you aren't short on space and want to use Fast Startup.
What is your motherboard?
Thanks for clarifying Fast Startup and Fast Boot being 2 different, unrelated options. I had thought perhaps the 2 settings were linked and both had to be enabled to see a benefit.
I have an MSI board that has both "MSI Fast Boot" and regular "Fast Boot" settings (enabling MSI's version disables the regular "Fast Boot"). If I enable "MSI Fast Boot," I can't get into the BIOS without going thru the menu in Win10...that's probably where the extra second shaved off the startup time comes from. If I enable "Fast Boot", while I don't get the MSI splash screen, I can still hit Del and get into the BIOS. The MSI splash screen is gone regardless of Fast Boot as long as I'm in UEFI-only mode.
I tried to measure the boot time difference with Fast Boot enabled and disabled, and I couldn't measure the difference. So it's more academic interest at this point.
I disable hibernation because I hear it's not so great for SSDs. And I only use sleep mode because it's faster and have PC connected to a battery backup. I wonder how much faster Fast Startup would be anyways if boot drive is SSD?