Probably the "English is a dual language with lots of words that mean the same thing because half are from French and the other half are Anglo Saxon" thing again. There are loads of words like this, there was an article about it on HN the other week
No, not whatsoever. "Camarade" is the French word they both stem from, and the spelling "comradery" is the (North) American variant which some sources describe as an error and some not.
It's the U.S. vs England spelling thing again, except this time the U.S. spelling doesn't seem to be catching on, for some reason.
To get a feel for the whole thing in Ngram I looked at "labor,labour", "color,colour" and "organize,organise" and for each one the U.S. spelling was winning by a little or by loads, but "camaraderie" heavily dominates "comradery" in terms of usage. So, a little bit mysterious, maybe.