Do they all talk at the same time?
A good point but most would think of the two the same. I know I had a hard time getting some ideas across on some research I was doing until I separated these two concepts out. Then people started to understand.
As in they're independent of each other?
The answer would be no. Concurrency doesn't require parallelism but parallelism require concurrency.
The second answer to this quora link explains it way better than I can. https://www.quora.com/What-is-the-difference-between-concurr...
I don't think it does. For example in a SIMD system there is parallelism, but no concurrency. Operations are being performed in parallel, but there is only a single program (SI..) and no concurrent tasks.
http://composition.al/blog/2014/11/24/yet-another-blog-post-...