I would remove the word "simultaneously" from the concurrency definition. Two threads can be executing concurrently on the same processor - strangely, the next sentence seems to acknowledge this. My personal definitions, based on my experience in systems and high performance computing research:

Parallelism: simultaneous calculations executing in the service of a single problem, usually with the goal of improved performance.

Concurrency: executions in the same time granularity, but not necessarily simultaneous. Also not necessarily in the service of the same problem, but some form of synchronization is required.