as has been stated, there appear to be cultural differences.
I am only speaking for the UK i guess, but over here, a roach is both. it is either used in reference to the small plug at the end, typically rolled up magazine cover etc, and it is also referred to in the context of an old horrible joint end, the leftovers of a smoke. "just let me roll a roach" being the former, and "i've a roach if you're desperate" being an example of the latter. we are used to it so can easily differentiate between uses.
in the states a roach is simply the left over joint from last night, but i guess roach smoking is vaguely more acceptable based on the fact that Americans don't roll with tobacco. in the UK we do so you can immagine it's a little bit nastier than purely leftover green. you got all the tar and everryyyyyything in there, yum! :S