The question was " what exactly would the "Stop" button do? Stop what?"Yeah, cause people do that so often that a dedicated button makes sense.
Other things to consider. Stop recording what? It doesn't really stop recording anyway, it just stops saving the recording and resets the live buffer for that tuner. Th only way to stop recording w/o shutting down is to put the TiVo in standby or tune to an "empty" channel.
Stop makes sense for a VCR, not for a DVR.
The question was not would it make sense to have a dedicated button.
But since you are apparently asking that now....
Perhaps not for you, but I stop recordings and playback nearly every time I use a DVR. In the old HDUI system I would hit left near the end of a program to stop playback, and when recording right-select to stop recording (recording meaning saving the playing program to a file that is stored in My Shows). So in a way a Stop button makes more sense to me then context sensitive use of Left or Right.
That being said I was not arguing for or against one, only answering the simple question - what would stop do....