Well, I have something to learn here then.   I thought Hibernate and Standby would be the same.  
On the laptop the Power Options/Advanced tab gives me a ComboBox "When I press the sleep button" with 2 options - Standby and Power Off.   I've had Standby selected and when I press it, I get "Preparing to Standby ... " and then it goes blank and I press the button again to bring it back.  Very convenient.  I also was under the impression that it powers down when in Standby.  I can do it at the office and go home and when I get home the battery has lost only a couple of percent.
I just tried it on the desktop, where the only combo is for "When I press the power button on my computer" and if I select Standby and hit the power button, instead of rebooting it goes blank until I hit the power button again, and it comes back.  But the fan certainly continues, so it's not powered off.
What I'm wanting is to turn it "off" during the day or overnight or any time I'm away for a length of time, just to save the electricity, even if it's a small amount.  But it's 2 and a half minutes to boot up if I really turn it off, and I would like the convenience of the really quick return of the laptop.
So what's the best solution here?