The minis auto "sleep"... You get the hit tivo prompt bouncing around the screen. This mode isn't reflected in the led... You can turn it off in the settings, I did. The minis are pretty efficient, so the standby mode in the menu isn't going to make a huge difference.
Standby on the full box has been discussed at length on here. It pretty much just turns off the outputs. One upside is that the box will ignore emergency broadcasts, depending on how your community broadcasts them. Scheduled recordings still record etc, so the power savings is relatively small.
-Roamio Pro/Slide Pro
-Stream (Gotta go unplug the sucker one of these days!)