An important distinction was overlooked in the 2006 entries about register & der Registerzug. As in the separate 2011 thread (link above), first get clear about distinction between das Register (set of organ pipes) vs der Registerzug (a knob used to activate a set of organ pipes). Then note that English-speakers often say "stop" for either of those meanings.
As a pipe organist with fluent German but English as mother tongue, I suggest this when translating from English to German:
register-->das Register [but NOT der Registerzug]
stop-->das Register, der Registerzug.
Translating from German to English, I suggest:
das Register-->stop, rank, register (with register being said much less often in English than the alternatives);
der Registerzug--> drawstop, stop knob, stop