Not really. There are differences.
In my experience the following happens:
With Sleep the hard drive powers down, etc. and the monitor
goes into power save mode. The contents of memory are
retained in RAM, and will be lost if there is a power
outage. It can be woken quickly by mouse movement or
keyboard activity (possibly dependent on Power settings).
With Hibernate the contents of RAM are written to disk
and the system is powered down. Upon power up the saved
contents are restored to RAM from disk. So memory contents
are preserved even if there is a power failure.
On both Sleep and Hibernate all open processes are preserved
between shut down and start up, but with Sleep those contents
could be lost in the interim.
Hibernate can be added to the menu via the Win 10 settings.
Image is from Win 10 21H2 desktop.
[i]"To set your PC so it hibernates:
Select Search on the taskbar, type control panel, and select it from
the results.
Select System and Security.
In the Power Options section, select Change what the power buttons do.
Select Change settings that are currently unavailable.
In the Shutdown settings section, select Hibernate."
[/i]
Shut down, sleep, or hibernate your PC
https://support.microsoft.com/en-us/windows/shut-down-sleep-or-hibernate-your-pc-2941d165-7d0a-a5e8-c5ad-8c972e8e6eff
I gather that Shut Down with FastRestart enabled is essentially
Hibeernate. So if one turns off FastRestart then Shut Down will
result in the loss of memory contents. Adding Hibernate to the
menu choices gives you the option to still retain RAM contents
during a shut down if desired.
The way I see it from the view here anyway.
Standard disclaimer applies: “Your Mileage May Vary”