Toggle - one button that performs a different function each time it's pressed.
Power Toggle - one button that turns a device on, then off, then on, etc.
Discrete - one button (or command) that always does the same thing.
Discrete on/off - two buttons (On and Off). ON always turns the device on and if it's already on does nothing. Same for OFF. Discretes allow you to resend the command multiple times with no consequences. Toggles can only be sent once.

Input - for TVs and A/V receivers mostly, these are the various sources that you can switch to. A TV usually has different inputs for different connection types (S video, DVI, HDMI, component, composite). An A/V receiver usually has different inputs for different components (TV, DBS, DVD, Tuner, Aux, etc.). You have to set up each device so the harmony knows which inputs are available and how to select each one. Then you tell each activity which input to use for each device and the harmony will automatically select the correct input when you go to that activity.

I think the easiest solution to your problem is to simply leave the DVR on all the time. Most DVRs are designed that way anyway. Then you can hit OFF upstairs which will turn off the TV but leave the DVR on, then go downstairs and select watch TV again which will turn on the TV downstairs.