It really doesn't require to be into the music to know the difference. Its easy to tell the difference if you pay attention enough to the music.
This! I think there's a distinct difference in the two styles, you will quickly pick up on it, if you compare a couple of tracks from some of the legendary names in both genres. Keep in mind, there are different types of black metal (old school, symphonic, etc) and there are different types of death metal (Florida, Swedish etc) and to makes more a little more complicated, there are bands who mix both genres (Behemoth and Belphegor to name a couple).
But try to compare some videos from a couple of the big names in
black metal like
Emperor, Darkthrone (except tracks from "Soulside Journey" which is actually a death metal album *sigh*),
Burzum,
Dimmu Borgir etc with some big names from
death metal like
Morbid Angel,
Obituary,
Cannibal Corpse,
At The Gates etc and you'll quickly notice some clear differences between the two genres (but of course also between the individual artists, even within their genres).