They are both processors and it's not called an i7 core, it's a core i7. The "Core" part of Core i7 is just a name. The lower end i7's (800s) are quad cores. The higher end i7s (950) are quad cores with 8 threads. The top of the line i7's (970, 980x) are 6 cores, 12 threads.
So what is the difference between a core and a thread you may ask? Simple.
Intel uses a technology called "Hyper-threading" it uses one core but has two "threads" running though each. It's kind-of like splitting a core in 2 weaker ones from a non technological standpoint..