I have six devices connected to my integrated. I believe only the two analogue devices can be powered off "completely" of "fully". The four digital ones are each moved to a "standby" state regardless of the labeling on the units or the remotes, whether it's "power", "standby", "on", "off", etc.; accordingly, there's no standard labeling across or even within devices, that is, between the units and their remotes. They all go into a standby, lo-consumption mode, regardless.
Thus, our devices have something like the following notations in their manual's opening pages:
"The unit is not disconnected from the AC power source as long as it is connected to the wall outlet, even if the unit itself is turned off. This state is called the standby mode. In this state, this unit is designed to consume a very small quantity of power." Or, "The player is not disconnected from the AC power source (mains) as long as it is connected to the wall outlet, even if the player itself has been turned off."
If you read further, you find reference to the units complying with international standards/requirements that units consume tiny amounts of power in such standby modes. I've seen a .5-watt consumption claim in one of my unit's manuals.
If you require truly off, pull the plug(s). I power-down after every use. Almost always that means the integrated and one other device. (My integrated has "link" and "trigger" connections/features that I've not used.)