The terms are used interchangeably - generally depending on what part of the country you are from. Both are some what derogatory in their meaning.
However - as more and more things in this world become "hybridized", there are now what some would call "breeds" out there that actually have Cur in the name, i.e. Black Mouthed Cur, Ozark Mountain Cur, and some I'm sure I haven't heard of. And since the CKC will register anything - this leads people to believe that they are getting something special. Much like the current craze for designer dogs.
We have what we lovingly refer to as, "ABD's" - Alabama Brown (or Black) Dogs where I am, but never in front of the client.
The most politically correct term for these would be a "mix", or "mixed breed".
Hope this helps!
Erika Vinson, LVT
ICU/ECC Technician
Dept of Clinical Sciences
Auburn University College of Veterinary Medicine