You can handle multiple concurrent connections/requests on a single CPU core; but that would not classify as parallel processing. So the term 'parallel' is more specific than 'concurrent'.
The paragraph under 'Introduction' here https://en.wikipedia.org/wiki/Concurrent_computing seems to give a pretty good definition.
In French, the word 'concurrent' literally means 'competitor' - Which in our case implies competition for computational resources (E.g. specific memory locations) - On the other hand, the 'Thinking in Parallel' article talks about how to partition resources in a way which removes the element of competition between processes - So the word 'Parallel' seems fitting.
Concurrent is for separate entities working together in a coordinated manner. A prime example is threads working together on a work queue. Parallel is for a singular entity doing multiple things at the same time. For example a vector instruction that does multiple additions at the same time.