Apple's understanding of the device being "off" / in stand-by is to just turn off the video output. The processor still runs at full speed and the hard drive still spins at normal speed. The only way to really turn it off is to pull the power cord!
This is true of the DVRs I've had too - a very small sample, admittedly, but I suspect it's broadly true of set-top boxes and the like. Why would it be different? The simplest implementation is to have "standby" simply appear to the user to have disabled the device's user-visible functionality. Consuming power is an externality for the vendors of such devices.