Cordite was used in British/Commonweath ammunition through WWII, though I will have to do some digging to find out when it stopped being used as the primary rifle propellent. The 50s I think, but am not sure, at this time.
Cordite does have a unique smell, different from other smokeless powders, and of course different from black powder.
"the smell of Cordite" has been a stock phrase in writing (particularly fiction) since the time Cordite replaced black powder. Today's writers continue to use it, because they either don't understand what it actually means, or more likely, they don't care.
Cordite came in long "cords" thin rods (think uncooked angel hair pasta), a bundle of them were inserted into the case and then cut off to fit. (by hand, with a knife) there are pictures from the Battle of Britain (1940) of English women making .303 ammunition this way.
If you shoot enough different powders, you will come to regconize that different powders have different smells after firing, even ones with very similar chemical construction can have noticeably different smells.
One example is IMR 4350. In my experience, it's powder smoke has an "ammonia" tang to it that other IMR powders do not.
Cordite has its own unique smell. I can't really describe it, only that is it something which, once you have smelled it you won't mistake for anything else.
Modern fiction writers, rarely smell gunsmoke of any kind, let alone Cordite, I think...